Prep: Place both types of wheat in a large bowl and have the vegetables and herbs ready.
Soak the Wheat: Cover the wheat with hot water, leaving the water about ¾ inch (2 cm) above the wheat. Let it hydrate for at least 2 hours.
Cook the Beef: While the wheat is soaking, season the ground beef with black pepper, allspice, finely chopped onion, mashed garlic, and salt.
Finish the Filling: Cook the beef with the mint and basil stems until browned and completely cooked through. Remove the herb stems and set the filling aside to cool.
Process the Wheat: Once hydrated, drain the wheat very well. Transfer it to a food processor with the mint leaves, basil leaves, cubanela pepper, onion, salt, black pepper, and allspice.
Blend: Process until the mixture is finely ground and holds together well enough to shape.
Shape: Lightly wet your hands and form a portion of the wheat mixture into an oval. Use your finger to create a hollow space in the center.
Fill: Add some of the cooked beef, then carefully close the opening. Smooth and gently press the outside until completely sealed.
Check the Shape: Make sure there are no cracks or openings before frying. A smooth, well-sealed quipe is much less likely to break apart in the oil.
Fry:Heat the oil to 350°F (180°C), then fry the quipes until deeply golden and crispy on the outside.
Drain: Transfer to a rack or paper towel-lined plate and let the excess oil drain before serving.