Place racks in upper and lower thirds of oven; preheat to 400°. Arrange bread slices in a single layer on a rimmed baking sheet and drizzle with 2 Tbsp. oil. Toss on baking sheet to coat, then arrange again in a single layer. Place broccoli and garlic on another rimmed baking sheet and drizzle with remaining 4 Tbsp. oil. Season generously with salt and toss to combine.
Place broccoli on top rack and bread on bottom rack and roast until bread is golden brown and crisp, 10–12 minutes. Remove bread from oven and continue to roast broccoli and garlic, tossing once, until broccoli is browned all over and garlic is tender, another 15–20 minutes. Let cool slightly.
Meanwhile, whisk honey, vinegar, and red pepper flakes in a small bowl.
As soon as garlic is cool enough to handle, squeeze cloves out of their skins and mash in another small bowl to form a paste. Add ricotta and mix well; season with salt and black pepper.
Spread ricotta over toasts and top with roasted broccoli. Arrange on a platter and drizzle with honey mixture.