You Should Cook With Extra Virgin Olive Oil and Here's Why Science Agrees
At tastings, I've had customers ask me if they should only use our oils for finishing or salads. I appreciate that they consider Beyond The Olive's oils "precious". They are, but I use them for everything - including frying. Now I don't deep fry anything, but I bring these oils up in temperature... and here's what I say - if you're burning the oil, you're probably burning your food too.
Here's the science:
Olive oils are tested for "free fatty acid". This isn't pH. pH can only be tested in a water soluble compound. Oil isn't water soluble, but you knew that already.
The LOWER THE Free Fatty Acid, the HIGHER the SMOKE POINT!
We have our extra virgin olive oils certified every year by the California Olive Oil Council (the COOC). Here are their criteria:

What does all of this measure? Purity!
Let's just focus on the FFA number. Richard Gawel, a researcher in Australia,* tested extra virgin olive oils and smoke point based on the free fatty acid of each. Here are his findings:

So you see the lower the FFA, the higher temperature you can cook at. The COOC insists their certified oils be at a maximum of 0.5 - Based on this chart, you could cook any COOC olive oil at least at 350 degrees Fahrenheit.
But our oils exceed this! Our extra virgins are below 0.2. I regularly cook with a wok on a gas stove and bring my pans up above 400 degrees Fahrenheit.

At Beyond The Olive, our goal since 2009 is trust and education in the ingredients we provide. Try our extra virgin olive oils and see for yourself. When you start with clean ingredients - they don't need "refining", because nature already has done that for you!
*Richard Gawel, Research Scientist, Adelaide, Australia. "The Intricacies of Olive Oil" — UC Agriculture and Natural Resources. Published: https://ucanr.edu/sites/default/files/2014-06/191586.pdf