Preheat oven to 425F and line a sheet pan with parchment paper.
Toss halved baby potatoes with 2 Tbsp olive oil, Italian seasoning, 3/4 tsp salt, 3/4 tsp garlic powder, and 1/2 tsp black pepper.
Spread potatoes on half the sheet pan and bake 20 minutes.
Meanwhile, toss broccoli florets with remaining 2 Tbsp olive oil, lemon juice, 3/4 tsp salt, 3/4 tsp garlic powder, and 1/4 tsp black pepper.
After 20 minutes, add broccoli to the other half of the pan.
Roast 15-18 minutes until broccoli is charred at edges and potatoes are fork-tender.
Sprinkle with parmesan cheese if using and toss to combine.
Serve immediately.