My instinct would be that food will cook quicker just before the water starts boiling because steam conducts heat slower than water and so when the food is in contact with the steam bubbles it receives less thermal energy.
This is absolutely the opposite of reality!
A steam bubble in contact with a body with a temperature less than
100°C will condense on this body, transferring about 540 cal/g!
In fact heating a wall by condensing steam is one of the most
efficient heat transfer methods.
But now your primary question: those noodles "cook" faster
where they experience the higher temperature. In a pot on a fire,
the surface of the water will be as low as maybe 80 or 90 degrees,
when bubbles raise at the bottom, but do not reach the surface yet.
(Again here: heat transfer by bubble evaporation is extremely
fast, same reasons as for condensation)
10 or 20 °C less are a lot when cooking noodles (wheat starch)
this may lower the reaction rate to half the value at 100°C,
or even lower (rule of thumb for such reaction).
Thermal conductivity: most amorphous solids/liquids have similar, low
heat conduction. Crystalline solids are medium, metals are much higher,
the thermal conductivity being related to the electrical conductivity.
Google for: Wiedemann Franz Lorenz.
Thermal conductivity of gases can be calculated using kinetic gas theory,
this was "triumph" for Clausius, Maxwell and Boltzmann.
Let's assume a one litre $1000{\,\rm W}$ electric kettle, filled with $0.5$ kilograms of water at $20^\circ \mathrm{C}$:
It takes 4.2 joules to warm one gram of water one degree Celsius.
So, to warm the $500$ grams of water $80$ degrees from $20$ to $100$ takes $168,000$ joules. The kettle will supply $1000$ joules per second, so it'll take $168$ seconds for the kettle to come to a boil.
During this time, the $0.5$ litres of air will expand by a factor of $\frac{373}{293}$, to a volume of $0.637$ litres. So in the almost three minutes of heating, only $0.137$ litres of air will be forced out through the whistle spout.
Now we're at the boiling point. It takes $2,280$ joules to vaporize $1$ gram of water. So the kilowatt heater will vaporize $0.439$ grams of water each second!
Those $0.439$ grams of water vapor will occupy around $0.750$ litres at $100^\circ$ Celsius. So this much gas will be forced out the spout each second...
$0.137$ litres of air in three minutes, vs $0.750$ litres of steam each second.. That explains the difference...
Best Answer
The bubbles explode because they superheat. The oil prevents the nucleation of steam bubbles you get when heating water in a pan, and the water drops turn to steam all at once and of course the steam expands explosively.
Even though water and steam are in equilbrium at 100°C there is a potential barrier to formation of a steam bubble. This is because small bubbles have a high pressure (the pressure is inversely proportional to the bubble radius) so you need a lot of energy to start a bubble. When you heat water in a pan you'll find steam bubbles nucleate at defects (e.g. scratches) in the pan surface. You'll often see streams of bubbles coming from the same point.
In your experiment the oil probably dewets the water droplets from the skillet so you have a water drop surrounded by oil and there is nothing to act as a nucleus. If you heat the oil slowly the water drops will superheat until eventually the temperature is high enough to nucleate bubbles. At that point part of the drop will turn into steam almost instantly and then expand explosively. You can work out how much of the drop vaporises by multiplying the superheating (i.e. the temperature - 100°C) by the specific heat of water, and then dividing this energy by the latent heat of vaporisation. As I recall, only a relatively small part of the drop vaporises, but of course this generates a large volume of steam
Even in ideal circumstances there is a limit to how far you can superheat the water. At some point the superheating is so great that nucleation will be triggered just by random fluctuations in the water. You couldn't superheat indefinitely even in perfectly pure oil and water in zero G. Obviously in your experiment the bubbles nucleate a lot earlier than this.
You get the same effect heating distilled water in a microwave oven. If you use pure water and a clean glass bowl there is nothing to act as a nucleus for the steam bubbles and the water can superheat. Sadly you often discover this as you remove the bowl as the vibration can induce nucleation and an explosion of steam - hopefully not in your face!