Cook the gnocchi according to the package instructions. Drain and set aside, reserving a cup of pasta water.
In a large skillet, cook the ground pork over medium-high heat until browned, about 5 minutes.
In the same skillet, add the torn mushrooms and the garlic and cook until tender, about 2 minutes. Deglaze the pan with a splash of dry vermouth, white wine, or water.
Separate two eggs and put the yolks into a small bowl or measuring jug. Add the red pesto and the parmesan cheese, and whisk to combine. Slowly add 100ml of hot pasta water to the yolk and pesto mixture.
Add the drained gnocchi to the skillet with the pork and mushrooms and stir to combine. Turn off the heat, add the yolky pesto mixture, and stir to incorporate.
Adjust the consistency with more pasta water and adjust the seasoning by adding salt and pepper if needed.
Serve with grated parmesan and fresh herbs, if desired.