Lay the tortillas flat on a plate or cutting board, cover with chocolate spread, and distribute the mini marshmallows over the filling area. Keep a small border clear around the edges so the melting marshmallows have room to spread.
Close each tortilla into a half-moon and coat the upward-facing surface with softened butter. A smooth, tacky layer helps the sugar and crumbs adhere instead of falling away.
Press brown sugar and graham cracker crumbs firmly onto the buttered surface, then lower that coated face onto a medium-heat skillet or grill. After about 2 minutes, the underside should look golden and smell toasted rather than sharply scorched.
Coat the exposed tortilla surface with butter, then press brown sugar and graham cracker crumbs onto it while the underside cooks. The upper coating should cling evenly, ready to brown after flipping.
Slide a wide spatula underneath, turn the quesadilla carefully, and cook the second side for another 2 minutes. Look for a golden exterior and marshmallows that have softened into a gooey filling.
Transfer the cooked quesadilla to a cutting board, slice into wedges, and serve promptly. The tortilla should still feel crisp while the chocolate and marshmallow remain soft.