Heat the oven to 425°F. Scatter the chopped bacon over a large rimmed sheet pan and bake 5 minutes, until it just starts to crisp. Transfer to a paper-towel-lined plate with a slotted spoon, leaving the rendered fat on the pan — that's the smoky base everything else roasts in.

In a large bowl, toss the broccoli florets, onion wedges, and gnocchi with the olive oil, garlic, 1 teaspoon Italian seasoning, 3/4 teaspoon salt, 1/4 teaspoon pepper, and the smoked paprika until evenly coated.

Spread the gnocchi and vegetables over the bacon fat in a single layer — give everything room so it roasts instead of steaming. Roast 8 minutes.

Season the chicken pieces with the remaining 1 teaspoon Italian seasoning, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Stir the pan with tongs, then nestle the chicken pieces among the vegetables and gnocchi in a single layer. Return to the oven.

Roast 8–10 more minutes, until the chicken is cooked through to 165°F, the gnocchi are golden and crisp at the edges, and the broccoli is charred at the tips.

Scatter the reserved bacon back over the pan, shower with the Parmesan and parsley, and rest 2 minutes. Serve straight from the pan with lemon wedges and extra Parmesan.