Preheat the oven to 425°F (220°C).
In a large bowl, combine the halved baby potatoes with 2 tablespoons of olive oil, 2 cloves of minced garlic, 1/2 teaspoon salt, 1/4 teaspoon black pepper, smoked paprika, and dried oregano. Toss to coat evenly.
Spread the potatoes on a large sheet pan in a single layer. Roast in the preheated oven for 12 minutes.
While the potatoes roast, in the same bowl, toss the broccoli florets with 1 tablespoon olive oil, 1 clove minced garlic, 1/4 teaspoon salt, and 1/4 teaspoon black pepper.
After the potatoes have roasted for 12 minutes, remove the sheet pan from the oven and add the broccoli florets. Toss gently to combine and spread evenly on the pan.
Return the sheet pan to the oven and roast for an additional 8 minutes.
Meanwhile, in the bowl, toss the shrimp with the remaining minced garlic, 1/4 teaspoon salt, 1/4 teaspoon black pepper, and crushed red pepper flakes.
After the broccoli and potatoes have roasted for 8 minutes, remove the sheet pan from the oven and add the shrimp in a single layer.
Return the sheet pan to the oven and roast for 5 minutes, or until the shrimp are pink and opaque and the vegetables are tender.
Remove the sheet pan from the oven. Drizzle the lemon juice over the shrimp and vegetables and sprinkle with chopped fresh parsley.
Toss gently to combine and serve immediately.