Makes 4 sandwiches.
For the spread:
3 Tbsp mayonnaise
1 Tbsp ketchup
1 tsp fresh chopped thyme or parsley leaves
1/4 tsp piment d'Espelette (or smoked paprika)
2-4 drops Sriracha sauce, to taste
Pinch of kosher salt
For the sandwiches:
8 slices crusty bread
4 portobello mushroom caps
2 Tbsp olive oil
Kosher salt and fresh black pepper
4 tsp goat cheese
4 1/4-inch slices ripe tomato
1 cup baby arugula leaves
Whisk together all of the spread ingredients in a small mixing bowl. Cover, and refrigerate until ready to use (can be made a day ahead).
Heat a panini press or stovetop grill pan, or an outdoor grill. When the pan is hot, toast the bread until light grill marks appear. Remove and set aside.
Paint the mushroom caps on both sides with olive oil, and sprinkle with salt and pepper. Place in your panini press (or grill pan, weighted down slightly with a brick wrapped in aluminum foil, or with a second cast iron pan), and grill for 4 minutes, or until the mushrooms are flattened and cooked through. Remove from the press or grill and set aside.
Assemble the sandwiches: Spread one side of 4 slices of bread with goat cheese. Spread one side of the other 4 slices with the smoked pepper spread. Divide the arugula between the 4 sandwiches, on top of the goat cheese. Top the arugula with the mushrooms and tomato slices. Close the sandwiches, press down slightly, and cut in half with a serrated bread knife.
Serve at room temperature, or let cool slightly, then wrap the sandwiches in plastic wrap and chill to serve later.