Process 1 coarsely chopped onion; 1 large Cubanelle pepper, seeded and coarsely chopped; 4 ounces ajíes dulces, seeded; 8 smashed and peeled garlic cloves; 1 cup recao leaves and tender stems; and ¾ cup cilantro leaves and stems in food processor until finely chopped, about 20 seconds, scraping down sides of bowl halfway through processing. Set aside ½ cup sofrito for this recipe; reserve remaining for another use.

Cook 6 ounces ground beef, ½ cup chopped onion, 3 minced garlic cloves, 1 teaspoon pepper, 1 teaspoon ground cumin, 1 teaspoon granulated garlic, 1 teaspoon dried oregano, and ¾ teaspoon table salt in 12-inch nonstick skillet over medium-high heat, breaking up meat with wooden spoon, until meat is no longer pink, 5 to 7 minutes. Stir in ½ cup sofrito and cook until fragrant, about 1 minute.

Stir in 1 tablespoon tomato paste and cook, stirring constantly, for 1 minute. Stir in 2 tablespoons water and cook until evaporated and tomato paste coats meat mixture, about 30 seconds. Remove from heat and stir in ½ cup pimento-stuffed green olives, chopped coarse, and ¼ cup cilantro leaves and stems, chopped. Let picadillo cool for 15 minutes.

Transfer picadillo to food processor and pulse until finely chopped, about 6 pulses, scraping down sides of bowl halfway through pulsing. Transfer to bowl, cover with plastic wrap, and refrigerate for at least 1 hour or up to 2 days. Divide picadillo into eighteen 1-tablespoon portions, and place on large plate. Cover and refrigerate until needed.

Meanwhile, heat ¼ cup vegetable oil and 1½ teaspoons annatto seeds in small saucepan over low heat, swirling occasionally, until bubbles begin to form around seeds and oil takes on deep red-orange color, 5 to 7 minutes. Remove from heat and let sit for 10 minutes. Strain oil through fine-mesh strainer into liquid measuring cup and set aside; discard seeds.

Fit clean food processor with shredding disk and shred 5½–6 pounds green plantains, peeled. Transfer shredded plantains to large bowl. Fit now-empty food processor with chopping blade. Add half of shredded plantains, half of annatto oil, and 2 teaspoons salt to food processor. Process until cohesive dough forms and begins to clear sides of bowl, about 90 seconds, scraping down bowl every 5 to 15 seconds, as needed, for first minute.

Transfer masa to clean, large bowl and repeat process with remaining shredded plantains, remaining half of annatto oil, and remaining 2 teaspoons salt. Transfer second batch of masa to bowl with first batch and stir to combine.

Line rimmed baking sheet with parchment paper and spray parchment generously with vegetable oil spray. Spray ¼-cup measuring dry cup with vegetable oil spray and use cup to portion 18 level ¼-cup scoops of masa (about 2½ ounces), respraying cup as needed; place scoops on prepared sheet. Divide any remaining masa evenly among scoops.

To shape alcapurrias, grease your hands well. Place one scoop of masa in your palm and pat into 4-inch patty. Place 1 portion of picadillo in center of masa patty and gently fold masa over picadillo to create half moon shape, pinching to seal. With gentle pressure, roll alcapurria between your hands to create tapered football shape, about 4 inches long. Return shaped alcapurrias to prepared parchment. Repeat filling and shaping with remaining masa and picadillo.

Set wire rack in rimmed baking sheet and line half of rack with triple layer of paper towels. Heat 3 quarts peanut oil in large Dutch oven over medium-high heat to 350 degrees. Add 6 alcapurrias to hot oil and fry until deep golden brown and hot throughout, about 5 minutes, gently nudging alcapurrias after 30 seconds of frying to keep from sticking to bottom of pot.

Transfer alcapurrias to paper towel–lined side of rack and let drain for about 30 seconds, then transfer to unlined side of rack. Return oil to 350 degrees and repeat frying twice more with remaining alcapurrias.