Juicy roasted portobello mushrooms make a luxurious sandwich for the vegetarians at your picnic table. Drape a slice of your favorite cheese over the top – sharp Vermont cheddar or mild Muenster both work well.
Heat oven to 400°. Brush mushrooms with olive oil and sprinkle with salt and pepper. Place on a baking sheet, gill side down, and cook about 8 minutes on each side (these are also great grilled). Remove from oven and cut into ½-inch strips. If possible, use while still warm.
In a small bowl, combine mayonnaise, lemon juice, and dill. Spread a thin layer of the mayonnaise on one side of bread slices. Divide ingredients among 6 slices of bread, layering them in this order: cucumber, sprouts, avocado, mushrooms, and cheese (if the mushrooms are warm, the cheese will melt a little and hold things together). Top with remaining slices of bread or serve open-faced.