Stir the mayonnaise, chile sauce, mustard, lemon juice and smoked paprika together for the comeback sauce.
Mix the cheddar, cream cheese and pimentos in a separate bowl until spreadable but still textured.
Heat a steel griddle or cast-iron skillet over high heat until faintly smoking and toast the split buns for 1 minute.
Place 4 cold beef balls on the hot surface, season them and immediately press firmly through parchment to 1/4 inch thick.
Cook untouched for 90 seconds until crisp at the edges; do not re-smash, then scrape, flip and cook for 60 to 90 seconds until 160°F.
Repeat with the remaining beef and spread 2 tablespoons pimento cheese over each of the final 4 patties for the last 30 seconds.
Spread comeback sauce over each bun, add lettuce and stack one plain patty beneath one pimento-cheese patty.