In a small bowl, combine the ricotta, lemon zest, thyme, salt, pepper and garlic. Add about 2 tablespoons EVOO. Slather it generously on the roll bottoms. Fold and quarter the sliced meat to ruffle it and arrange it on top on the cheese. Tuck in the sliced capers and onions among the folds. Toss the greens with juice of 1/2 a lemon and a drizzle of EVOO, about 1 tablespoon. Arrange on top of the meat and set the bread top in place.
Press panini to crust the bread and warm the ricotta. Split and serve.