Cook gnocchi in salted boiling water until they float to the surface (~2–3 minutes). Drain well and pat dry.

Meanwhile, melt butter in a skillet over medium heat. Let it foam and begin to brown slightly, developing a nutty aroma and golden flecks.

Add sage leaves to the butter and fry briefly until crisp. Remove sage leaves and set aside for garnish.

Add a little olive oil if desired to help crisping, then arrange gnocchi in a single layer in the skillet. Sear without stirring until bottoms are golden (5–6 minutes), then gently flip and brown on the other side.

Pour the browned butter back over the seared gnocchi and toss to coat evenly. Season with salt and pepper, and sprinkle in grated Parmesan.

If using optional add-ins like vegetables or sausage, stir them in now to warm through.

Finish with lemon zest or a squeeze of fresh lemon juice if desired. Toss gently to combine.

Transfer to plates, garnish with crisp sage leaves and extra Parmesan cheese, and serve immediately.