Preheat the oven to 400 degrees. Line a large baking sheet with parchment paper, and spread the chopped sweet potatoes into an even layer. Drizzle 1 tbsp of the oil over them, season with a pinch of salt and pepper, and roast for about 30 minutes. They should be soft enough to easily stick a fork through when they are done.
Transfer the potatoes into a food processor, add 1 tbsp of the butter, and about 1/4 cup of the milk. Turn on the food processor and puree until the mixture becomes smooth and creamy. You can add a little bit more milk if it is too thick, but that depends on how you want the texture to be. Make sure you don't puree this for too long, as it will make the potatoes a bit gummy. Just blend until creamy.
Preheat a large skillet (I used cast iron) over medium-high heat. Prepare the brussels by removing the outer leaves, chopping off the ends, and then cut them in half. Add 2 tbsp of olive oil and 1 tbsp of the butter to the skillet, then add in the brussels sprouts. Season with a small pinch of salt and pepper, toss to coat, and let them cook for about 4-5 minutes, only stirring occasionally to make sure they brown.
Once they are starting to turn brown and char a little bit on the outside, add the shrimp to the skillet. Season with the paprika, another small pinch of salt and pepper, and add the garlic. Toss to coat, and let the shrimp cook for 3-4 minutes, until the shrimp turn opaque and start to get little char marks on them.
To assemble the dish, spoon some of the potato puree onto a plate, and then top it with the shrimp and brussels mixture.