In a food processor or blender, combine the arugula, walnuts, cheese, garlic, and ½ tsp. of the salt and process until well blended. Slowly add the oil while processing it until it is creamy and smooth.
Sprinkle both sides of the cutlets or tofu slices with 1/8 tsp. of salt and the pepper.
In a large heavy skillet, melt the butter over a medium-high heat. Once the butter has melted, add the cutlets or tofu, turn the heat down to medium, and cover with a lid.
Flip the cutlets after 3 minutes (if using tofu, cook them for 6 – 7 minutes before flipping) and cover again.
Cook for an additional 3 – 4 minutes (for either the pork or the tofu) or until cooked through and golden brown. (If the cutlets or tofu slices are getting too browned on their outside, reduce the heat under the skillet.)
Serve the cutlets or tofu with a dollop of pesto on top or on the side for dipping.