Active time: 25 minutes Total time: 1 hour 20 minutes
Preheat oven to 350°. In a roasting pan, combine 1 cup water, 1 Tbsp. butter, sage stems, and bay leaves. Season cut sides of squash halves with ½ tsp. each salt and pepper and place in pan, cut sides up, evenly spaced. Bake until squash is tender but still holding its shape, about 50 minutes, basting a few times with liquid in pan.
Transfer squash halves to a work surface and let cool about 5 minutes. Cut in half again to form 8 quarters. In a large nonstick skillet, melt 1 Tbsp. butter. Add sage leaves and cook over medium heat until crisp, about 1 minute per side. Transfer sage to a plate. Add 1 Tbsp. butter to skillet and melt. Add half the squash quarters, cut side down, and cook over medium-high heat until browned, about 2 minutes. Turn squash to other cut sides and brown. Transfer squash to plates. Repeat with remaining 1 Tbsp. butter and squash.
Add vinegar to skillet and boil over high heat, scraping up browned bits, 1 minute. Season with ¼ tsp. each salt and pepper and pour over squash. Spoon 2 Tbsp. ricotta in each squash quarter, scatter reserved crispy sage on top, and serve.