For the pickled habanero onions: Combine 1/2 cup water, the lime juice, vinegar, sugar, salt and habanero chile in a medium saucepan. Boil the vinegar mixture until the sugar is dissolved. Remove the saucepan from the heat and cool for 5 minutes. Put the onion slices in a small bowl. Pour the warm vinegar mixture over the onions and toss to coat. Cover the bowl and refrigerate for at least 4 hours and up to 48 hours, stirring the mixture a few times.
Meanwhile, for the mole: Heat the oil in a saucepan until it begins to shimmer. Add the onions and cook until soft, about 4 minutes. Add the garlic and cook, about 30 seconds. Stir in the chicken stock, pureed tomatoes, chipotle, molasses, honey, maple syrup, ancho chile powder, New Mexico chile powder, cinnamon, allspice, chile de arbol and ground cloves. Sprinkle with salt and pepper. Bring the mole to a simmer and cook, about 5 minutes. Add the almonds, chips, mangoes and raisins. Cook, stirring occasionally, until the mangoes are soft and the mixture is reduced by half, about 30 minutes. Carefully transfer the mixture to a blender and blend until smooth. Return the mixture to the saucepan over high heat. Add the chocolate and cook until reduced to a sauce consistency, about 10 minutes. Sprinkle with salt and pepper.
For the burgers: Preheat the grill to high for direct heat. Divide the ground meat into 4 equal portions, 6 ounces each. Form each portion into a 3/4-inch burger. Make a deep impression in the center of each burger, using your thumb. Brush the burgers on both sides with the oil and sprinkle with salt and pepper. Grill the burgers until golden brown and slightly charred on both sides and cooked to medium doneness, about 8 minutes. About a minute before removing the burgers from the gill, top with the Manchego and cover the grill. Transfer the burgers to the buns and top with a large dollop of the mole sauce, a few slices of avocado and some of the pickled habanero onions.