COMBINE all ingredients for pesto in food processor and pulse until finely chopped, seasoning with salt and pepper, to taste. Pesto can be made up to 2 days ahead and stored in refrigerator until ready to use.
MELT 1 tablespoon of butter in large skillet over medium-high heat. Add ham and cook until crisp, 2-3 minutes. Remove ham from skillet and set aside on a paper towel
ADD remaining butter and gnocchi to skillet. Cook gnocchi 5-7 minutes, until starting to turn golden brown. Remove from skillet and set aside with ham.
REDUCE heat to low and add pesto and heavy cream. Cook sauce, whisking constantly for 1-2 minutes, until combined and thickened. Stir in gnocchi and cook for 1-2 minutes.
REMOVE from skillet and serve topped with crispy ham and Parmesan.