Summer Squash Parmigiana Sandwich

Name: Summer Squash Parmigiana Sandwich
Ingredients: 1 chayote, ¼ inch sliced; 2 medium zucchini, ¼ inch sliced; A pinch of pepper, ground; A pinch of sea salt, ground; 1 clove garlic, minced; Olive oil for drizzle; 2 tablespoons parmigiano-reggiano, grated; 4 tablespoons or so, quatro formatio; (or equal amount of grated provolone or mozzarella); 2 tablespoons marinara or seasoned tomato sauce; 1 6″ roll, or equivalent; 2 teaspoons butter, softened; ½ clove garlic, minced; A pinch of salt if desired