Make romesco: Using blender at high speed, puree all sauce ingredients except parsley and Wisconsin alpine cheese. Blend until smooth. Place romesco in small bowl; fold in parsley and alpine-style cheese. Set aside.
Make picada garlic butter: Whisk all ingredients and set aside.
Assemble sandwiches: Preheat skillet over medium heat. Spread thin layer of picada garlic butter on 1 side of each bread slice. Place 1 1/2 slices each of fontina and aged cheddar on 4 bread slices, buttered-side-down. Top with rolled-up slices of Serrano ham, 3 slices on each bread slice. On unbuttered sides of 4 remaining bread slices, place 1 1/2 slices each of Wisconsin fontina and sharp cheddar cheeses. Top with 2 tablespoons romesco.
Heat large skillet. Working with 1 each of the ham- and romesco-topped bread slices at a time, place buttered-side-down in skillet. Grill until bread is golden and cheeses have melted. Arrange escarole over Serrano-topped slice. Flip romesco-topped bread slice onto ham slice. Repeat procedure to make 4 sandwiches.
For Romesco Sauce:
- 1 1/3 cups sliced, blanched almonds, lightly toasted
- 2/3 cups drained jarred roasted red peppers, thoroughly patted dry with paper towels
- 7 tablespoons olive oil
- 4 teaspoons sherry vinegar
- 3 large cloves garlic
- 1 teaspoon kosher salt
- 4 teaspoons smoked paprika
- 1/4 cup chopped parsley
- 1 1/3 cups Wisconsin Alpine-style cheese, finely grated
For Picada Garlic Butter:
- 4 tablespoons butter, softened
- 1 tablespoon olive oil
- 2 large cloves garlic, minced
- 2 tablespoons sliced, blanched almonds, ground