For the beans: Place the beans in a saucepan and add cold water to cover by 2 inches. Bring to a boil, cover, and remove from the heat. Let stand for 1 hour, then drain.
Return the beans to the saucepan along with the onion, celery, carrot and bay leaf. Add water to cover by 2 inches. Slowly bring to a simmer over medium-low heat. (If you heat them too fast, the skins may break.) Adjust the heat to maintain a bare simmer and cook, uncovered, until the beans are almost tender, 20 minutes or longer, depending on the age of the beans. Add salt, to taste, and continue cooking until the beans are tender but not mushy. Remove from the heat and let cool in the liquid. (You can prepare the beans to this point 1 to 2 days ahead; cover and refrigerate.)
Preheat the oven to 300 degrees F. Drain the beans and discard the vegetables but reserve the liquid.
In a preheated casserole pan that can go from the stove top to the oven, pour in 1/4 cup olive oil, add garlic cloves and allow to caramelize, about 1 to 2 minutes. Stir in tomato puree, simmer about 10 seconds, then add beans and white bean liquid. Sprinkle top with cherry tomatoes, thyme, parsley, red pepper flakes, and 1 cup olive oil. Season with salt and pepper, to taste. Bake, uncovered, for 30 minutes.
Remove from the oven and let rest for 15 to 20 minutes, then stir in the remaining 1 tablespoon olive oil, taste for seasoning, and serve over orecchiette pasta.
When the recipe calls for swirling in 1 tablespoon olive oil at the end, that's the moment to get out your best extra-virgin olive oil.