Bake tater tots according to package instructions. Remove from oven and press down on the tater tots with a cooking utensil to flatten them. Set aside.
Meanwhile, cook the ground chorizo in a small skillet over medium heat, breaking apart into small pieces. Cook until browned and cooked through. Drain grease and transfer to paper towel-lined plate or bowl.
Butter one side of each slice of Potato Bread. Place buttered sides down on a cutting board and spread Bacon Jam onto the other side of each slice. Onto two of the slices, sprinkle ¼ cup of shredded cheese followed by the smashed tater tots, cooked chorizo, and remaining cheese. Top with the two remaining slices of bread, Bacon Jam side down.
Heat a clean skillet to medium heat and grill sandwiches, in batches if necessary, until cheese is melted and both sides are browned, about 4-5 minutes total.