Make the garlic butter
Add the butter, minced garlic, and parsley to a microwave-safe bowl.
Microwave until melted, then stir well. Set aside while you prepare the filling.
Soften the onion
Heat olive oil in a large skillet over medium heat.
Add the sliced red onion and cook for about 2 minutes, stirring often, until slightly softened.
Add the garlic
Stir in the minced garlic and cook for about 30 seconds.
Keep the garlic moving so it smells fragrant but does not burn.
Make the BBQ chicken filling
Add the shredded chicken, paprika, Worcestershire sauce, and BBQ sauce to the skillet.
Stir until the chicken is fully coated and heated through, about 2 to 3 minutes. Taste and season with salt and pepper if needed.
Butter the bread
Lay the bread slices on a clean work surface.
Brush one side of each slice with the garlic butter. Turn the slices over so the buttered sides face down.
Build the sandwiches
Place one slice of Havarti on 6 pieces of bread.
Divide the BBQ chicken mixture evenly over the cheese. Add another slice of Havarti on top of the chicken, then close with the remaining bread slices, buttered side facing out.
Cook until golden
Place the sandwiches in a large nonstick skillet over medium heat.
Cook for 3 to 5 minutes, until the bottom is golden and crisp.
Flip and finish
Carefully flip the sandwiches.
Reduce the heat to medium-low and cook for another 3 to 5 minutes, until the second side is toasted and the cheese has melted.
Slice and serve
Let the sandwiches rest for 1 minute, then slice in half.
Serve warm with chips, fries, coleslaw, pickles, or extra BBQ sauce.