Make annatto oil: Combine annatto seeds with 0.25 cup taken from the vegetable oil in a small saucepan over low heat until the oil turns deep orange-red, 5β7 minutes; cool, strain, and set the annatto oil aside.
Measure the kosher salt; reserve 1 tsp for the masa and 0.75 tsp for the filling.
Warm 1 tbsp annatto oil in a large skillet over medium heat. Add white onion, green bell pepper, and carrot; cook, stirring, until softened and translucent, 5β7 minutes.
Stir in garlic, then add ground beef; cook, breaking it up, until no longer pink, 6β8 minutes. Drain excess fat if needed.
Add russet potato, tomato paste, ground cumin, dried oregano, black pepper, and the reserved 0.75 tsp salt; cook 2 minutes. Pour in chicken broth and simmer, stirring occasionally, until the potato is tender and most liquid is absorbed, 8β10 minutes. Taste and adjust seasoning if needed.
Stir in fresh cilantro. Spread the filling on a plate or tray to cool to room temperature, 10β15 minutes.
Make the masa: In a mixing bowl, combine masa harina and the reserved 1 tsp salt. Add 2 tbsp annatto oil and lard, then pour in warm water gradually while mixing until a soft, pliable dough forms. Knead briefly, 1β2 minutes, cover, and let rest 15 minutes.
Divide the dough into 12 equal balls (about 2 tbsp each). Working one at a time, press each ball between plastic in a tortilla press or roll to a 5β6 inch round.
Place about 2 tbsp cooled filling on one half of each round. Fold into a half-moon, press out air, pinch firmly to seal, and crimp the edge with a fork.
Heat the remaining oil in a deep pot to 350Β°F. Fry pastelitos in batches without crowding, turning once, 3β5 minutes total, until deep golden and crisp. Transfer to a rack or paper towels to drain.
Serve hot with cabbage, tomato sauce, and lime wedges.