Using the sauté function (on low, if possible), heat the oil in the pressure cooker pot. Stir in the garlic and cook until just turning golden, about 2 minutes. Stir in the marinara sauce, 2 tablespoons of the Parmesan, and 1/4 teaspoon pepper.
Increase the sauté heat to medium.
Season the chicken with the salt, oregano, and pepper to taste. Nestle the cutlets into the sauce, overlapping as little as possible, then spoon the sauce over to cover the chicken.
Lock the lid into place and cook on low pressure for 3 minutes. Manually release the pressure.
Sprinkle the mozzarella and the remaining 1 tablespoon Parmesan evenly over the chicken. Cover the pot with the lid (but don’t lock it on) and let it sit for 4 to 5 minutes to melt the cheese.
Serve as is or, for deeper flavors and a little bit of crispiness, broil the cheese until golden and bubbling: Heat the broiler with a rack 4 inches from the heat source. Scoop the chicken and sauce into a greased small rimmed baking sheet, trying to keep the cheese on top. Broil until the cheese has browned, 2 to 3 minutes. Sprinkle with basil, if desired.