IN a large bowl, place masa, lard, baking powder, flour and salt. Mix with hands. Add milk in small increments and continue to mix with hands. Knead the dough until malleable and does not stick to hands.
COVER bowl with plastic wrap. Take a piece of masa, about the size of a lemon and form a cylinder with the palms of your hands. Place masa cylinder between two plastic sheets and press flat with a tortilla press or rolling pin to 1/8” thick. With a small knife, trim rough edges of huarache for a cleaner finish (optional).
HEAT comal, grill pan or skillet over low-medium heat. Place huarache on hot skillet and cook for 2 minutes on each side or until masa begins to slightly burn. Remove and place on a plate and cover with cloth napkin. Repeat with the rest of the dough until all dough has been used.
IN a medium saucepan, heat cactus strips for 5 minutes. Spoon 4 tablespoons of cactus strips on each huarache, sprinkle with pieces of cheese and sprinkle with chopped grape tomatoes.