Drain beans and place in a large heavy pot along with halved onion, Parmesan rind (if using), halved head of garlic, bay leaves, and 2 tsp. salt. Add water to cover by two inches. Bring to a boil, reduce heat, and simmer until beans are tender, 1-1 ½ hours.
Meanwhile, cook bacon in a large skillet over medium heat, turning occasionally, until brown and most of fat has rendered, 8-10 minutes. Transfer to a plate with tongs or a slotted spoon.
Add thinly sliced onion, shallot, thyme sprigs and three-fourths of chopped garlic to pan drippings in skillet. Season with salt and pepper. Cook, stirring occasionally, until onion is starting to caramelize and is very soft, 10-15 minutes.
Add wine, bring to a simmer, and cook, stirring occasionally, until liquid is almost completely evaporated, about four minutes. Remove from heat and pluck out thyme sprigs.
Preheat oven to 400 degrees. Drain beans, reserving cooking liquid. Transfer beans to a large bowl and mix in bacon, onion mixture, thyme leaves and 1 ½-2 cups cooking liquid (this will be most of it; mixture should be consistency of stew). Season with salt and pepper. Transfer beans to a shallow 1 ½-qt. baking dish.
Mix breadcrumbs, oil and remaining chopped garlic in a medium bowl. Season with salt and pepper. Scatter over beans. Bake until liquid is thickened and bubbling and crumbs are golden brown, 45-55 minutes. Let cool slightly before serving.