To a large non-stick skillet or cast iron pan, add 1 tablespoon oil and heat on medium-high heat.
Add gnocchi and pan fry for 2-3 minutes. Flip, and fry for an added 2-3 minutes until golden brown on both sides.
Remove from pan and allow to drain on paper towel lined plate.
To same skillet, add 1 teaspoon oil and heat on medium-high heat. Add peppers and saute for 1-2 minutes, until fragrant. Add garlic and saute for 30 seconds, do not allow to burn.
Add shrimp and saute for 4-5 minutes until opaque.
Reduce heat to low. Add pesto and red pepper flakes, stir to combine, encouraging pesto to adhere to the shrimp.
Add gnocchi to the skillet, then add Parmesan cheese, lemon juice and melted butter. Toss to combine and serve at once.