The genesis of this comes to me from Escoffier, and to him from "the bourgeois kitchens of Provence and is actually a Fondue of tomatoes." I have made an altercation or two but the spirit remains his.
Peel, seed and chop the tomato meat. Save the skins and seeds for a stock or soup base.
Peel the garlic clove; pick and chop the lemon thyme leaves.
Chop the tomatoes into uniform sized of approximately 1 inch cubes.
Heat the extra virgin olive oil in a deep, heavy bottomed pot, to nearly smoking. You will see the oil "walking," that is, lines of movement in the oil.
Add the garlic, allow to cook just a few seconds to get browned and add the tomatoes. Please take great caution to avoid splashing the chopped lemon thyme and tomatoes into the very hot oil. It is best to place the tomatoes into a bowl which will fit into the pot and then, with an oven mitt on your hand to protect from steam, put the bowl as near the surface of the oil as you can and tip the tomatoes into the oil.
Stir the tomatoes immediately with a wooden spoon. Reduce the heat to low and let the tomatoes simmer for half an hour. Stir often until the heat reduces, then cover the pot and stir now and again.
The tomatoes will have broken down greatly but will still have some identity remaining. This is an excellent sauce for fish or chicken or even as a dipping sauce for fried zucchini sticks.
For those of you with La Guide Culinaire, this is recipe 72.
This sauce lends itself to accepting a variety of flavors, including anchovies and olives and rinse, salt-packed capers (the brined kind are okay, but the salt-packed have superior flavor).
Classical French purists will bulk and insist no change can be made. Remind them with kindness that Escoffier spent his whole life experimenting and tweaking and finding the best flavor and methods. Surely we can allow that he would approve of an improvement, especially if it tasted good and was cooked well.