Line a large baking sheet with parchment paper. Chop the vegetables as noted above. Place them in a bowl and mix with 1 tablespoon olive oil, 1/2 teaspoon garlic powder, 1/2 teaspoon oregano, and 3/4 teaspoon kosher salt. Pour onto the baking sheet in a single layer and bake for 13 minutes.
Pat the shrimp dry. In a medium bowl, mix the shrimp with 2 tablespoons olive oil, 1/2 teaspoon smoked paprika, 1/2 teaspoon garlic powder, 1/2 teaspoon onion powder, and 1/2 teaspoon kosher salt.
Add the shrimp to the baking sheet on top of the vegetables. Return the sheet pan to the oven and bake for 6 to 8 minutes until the shrimp is opaque and cooked through, depending on the size of the shrimp.
Remove from the oven. Sprinkle with the lemon juice, feta cheese, and chopped parsley. Serve immediately.