Give kids the important jobs of drizzling the olive oil, squeezing the lemon, and topping with Parm.
Preheat oven to 400°F. Bring a pot of salted water to a boil.
While water is coming to a boil, finely cut broccoli florets off the stalks into about 1/4-in. pieces, cutting from the floret end of each head. You should have about 4 cups. Reserve stalks for another use.
Pour olive oil into an 8×8-in. baking dish. Add garlic and place in the oven for 5 minutes. Carefully remove the pan from the oven, add shrimp and 1/2 tsp. salt, and toss to coat. Return to the oven and cook until shrimp are opaque, 9 or 10 minutes. Squeeze 1 lemon half over the shrimp and stir.
While shrimp are cooking, add orzo to the boiling water and cook according to package directions, stirring in the chopped broccoli for the last 2 minutes of cooking. Drain and return to the pot.
Pour the shrimp mixture into the broccoli-orzo mixture, squeeze in the juice of the remaining lemon half, and add the remaining 3/4 tsp. salt; stir to combine. Drizzle with more olive oil and top with red-pepper flakes and/or Parmesan, if using.