Prepare the adobo marinade: In a large bowl or resealable bag, combine soy sauce, vinegar, minced garlic, bay leaves, black peppercorns, brown sugar, and olive oil. Stir until the sugar dissolves.
Marinate the pork: Add the pork cubes to the marinade, ensuring each piece is coated. Cover and refrigerate for at least 2 hours, or up to overnight. Remove from the fridge 30 minutes before grilling so the meat comes closer to room temperature.
Prepare the grill: Light your charcoal grill (or preheat gas grill) to medium-high heat — about 400°F. You want direct and indirect zones for flexible cooking.
Cook the pork: Place pork pieces on the hotter side of the grill, leaving space between them for browning. Cook for 3-4 minutes per side until deeply caramelized and charred in spots. If using a large single roast, sear all sides first, then move to indirect heat and cook covered for about 20 minutes more. The internal temperature should reach at least 165°F before you remove it. Let rest for 5-8 minutes while you finish the onions.
Prep the onion leaves: Peel away the outermost layers of each onion, keeping the largest intact pieces whole — these are your "leaves." Trim the root end flat so the onions sit upright on the grill grate. Slice a thin layer off the top to create an opening for stuffing.
Make the esquite filling: In a mixing bowl, combine drained corn, mayonnaise, cotija cheese, lime juice, cumin, chili powder, and salt. Mix until creamy and well combined. Taste and adjust seasoning — you want it bright and savory with just enough tang from the lime and cotija.
Stuff the onions: Spoon the esquite mixture generously into each onion cavity, mounding it slightly above the rim. Pack tightly so it holds together when lifted.
Grill the stuffed onions: Place onions on the grill cut-side up over indirect heat for 8-10 minutes until tender and slightly charred on top. For extra char, move them directly over the flames for the final 2-3 minutes — watch closely to avoid burning the filling.
Serve: Remove onions from the grill and let cool for a minute before lifting out the filling with a spoon (or eat straight from the onion!). Serve alongside the adobo pork with extra cotija, cilantro, and lime wedges on the side.