Preheat the oven to 400ºF and line a large baking sheet with parchment paper or aluminum foil.

In a large bowl, toss the broccoli florets, shallot, and garlic cloves with a drizzle of olive oil, a big pinch of salt, and a few turns of freshly ground pepper. Toss to combine; if the broccoli looks dry, add a little more olive oil. Spread the vegetables on the prepared baking sheet in an even layer.

Roast the broccoli, shallot, and garlic for 20-25 minutes, stirring around halfway through. The broccoli should have some brown, crispy edges.

Add the roasted vegetables to a food processor, along with the sour cream, cream cheese, mayonnaise, paprika, and half of the cheddar cheese in a blender or food processor. If you like, add a few dashes of hot sauce. Pulse a few times to combine; season with salt and pepper to taste. The broccoli should be fairly small, but retain some of its texture — you may need to remove the blade and stir to completely combine.

Add the cheesy broccoli mixture to an 8”x8” square or 9” round baking dish, coated with olive oil. Spread the remaining shredded cheddar cheese over top, and bake for about 20 minutes, or until the cheese is melted and the edges are bubbling.

Serve warm with pita chips, pretzels, or anything else that you like to dip!