Preheat your oven to 400 °F. Place the cleaned and dried shrimp into a mixing bowl and set aside so they’re ready for seasoning.
In a small bowl, stir together olive oil, minced garlic, parmesan, smoked paprika, and black pepper. Mix until it forms a uniform paste-like coating.
Pour the garlic-parmesan mixture over the shrimp and combine so each piece is coated well. Spread the shrimp, zucchini, squash, and cherry tomatoes on a sheet pan in a single layer so they roast evenly.
Place the pan in the oven and roast for about 12 minutes. The shrimp should turn pink and firm, and the veggies should look slightly caramelized. Add a minute or two if needed.
Remove from the oven and sprinkle fresh basil evenly over the top. You can toss lightly to distribute flavors or leave as is for presentation.