Lightly butter outside of rye bread slices. Combine mayonnaise, Dijon and 1 tablespoon butter to create a sauce. Set aside.
Place bread slices buttered-side-down on work surface. Spread sauce generously over each slice. Place 2 slices havarti on 1 bread slice. Top with Braunschweiger slices. Sprinkle with arugula; place onion and avocado slices over arugula. Top with remaining havarti slices and other bread slice, buttered-side-up. Preheat griddle or skillet. Grill sandwich, flipping once, until bread is toasted and cheese begins to melt. Remove sandwich from heat and halve on the diagonal to serve.
- 1 tablespoon softened butter, plus additional for bread
- 2 slices rye bread
- 1/2 cup mayonnaise
- 2 teaspoons Dijon mustard
- 4 slices (about 4 ounces) Wisconsin smoked Havarti cheese
- 4 thick slices Braunschweiger
- Handful of arugula
- 1/4 red onion, sliced
- Avocado slices, thinly cut vertically