While the meat and potatoes are working, make the salsa verde: Set up a food processor or blender and fill with the herbs, garlic, shallot and red wine vinegar. Pulse to chop everything up then leave it on while streaming in the EVOO, until the mixture is the consistency of pesto. Season with salt and freshly ground black pepper, and reserve.
When the potatoes are just about ready, fill a lidded pan with about 1 inch of water and place over high heat. When the water is at a rolling boil, drop in the green beans and cover the pan. Cook the beans until crisp tender and bright in color, about 2 minutes. Drain the beans and toss the lemon zest and juice, capers and butter into the pan. Once the butter is melted, add the drained beans back into the pan, toss to coat in the lemon butter and season with salt and freshly ground black pepper.
Once the potatoes are finished, drain them and return them to the pot they were cooked in to dry out. Add the peas and ricotta to the spuds and mash everything up together. Season with salt and freshly ground black pepper.
Serve everything up family-style, passing the salsa verde at the table to pour over the chops.