3 tablespoons Dijon mustard
2 tablespoons mayonnaise
4 large portobello mushrooms, stemmed
2 tablespoons olive oil
Freshly ground black pepper
4 ounces smoked Gouda cheese, grated (about 1 cup)
4 brioche hamburger buns, split
4 ounces peppadew peppers, thinly sliced (about 1/2 cup)
1 cup loosely packed arugula
Heat an outdoor grill to medium-high heat (375°F to 425°F). Whisk together the Dijon and mayonnaise in a small bowl and set aside.
Brush mushrooms on both sides with the oil, then season with salt and pepper. Place the mushrooms on the grill stem-side down, cover, and grill for 4 minutes. Flip the mushrooms, cover, and grill until mushrooms are tender, about 4 minutes more.
Divided the Gouda among the mushroom caps. Arrange the buns cut-side down on the grill. Cover and cook until the cheese is melted and the cut sides of the rolls are golden-brown, about 1 minute more.
Place the bottom halves of the buns cut-side up on plates and spread with half of the Dijonaise. Top each with a mushroom. Top with the peppadews and arugula. Spread the cut side of the bun tops with the remaining Dijonnaise, place on the arugula to close the burgers, and serve.
No-grill option: You can also bake the mushrooms instead of grilling them: Heat the oven to 425°F. Place the oiled and seasoned mushrooms on a rimmed baking sheet stem-side down and roast until just tender, about 15 minutes. Flip them, fill the caps with the Gouda, and continue to bake until the cheese is melted, 2 to 3 minutes. Toast the buns in the oven.