Put beans in a large heavy pot with enough water to cover by 1 1/2 in. Bring to a boil over high heat, covered; then turn off and let sit 2 hours. Or, soak beans overnight at room temperature without heating.
Add enough water to pot now and through step 4 to cover beans by 1 in. Add bay leaves and bring to a boil, then reduce heat and simmer, covered, 30 minutes.
Meanwhile, heat 1/3 cup oil in a large frying pan over medium-high heat. Add chile flakes, onion, fennel bulb, and garlic and cook, stirring often, until onion softens, 5 to 6 minutes.
Add 2 tsp. salt and onion mixture to beans and cook until beans are barely tender, 20 minutes to 1 1/4 hours, depending on the type and age of beans.
Drain beans, keeping them a little bit brothy. Stir in parsley, pepper, and thyme and season to taste with salt. Top with a drizzle of olive oil and fennel fronds.
*Mediterranean bay leaves, the traditional type used in cooking, have an oval shape and milder flavor than California bay leaves, which are long and pointed and have a pungent flavor.