Preheat grill. Brush the mushrooms with 1/4 cup of the olive oil and season with salt and pepper to taste. Grill on both sides until golden brown and cooked through, about 10 minutes. Remove the mushrooms and slice thinly. Place the potatoes in a large bowl and add the mushrooms, onions and red pepper. Whisk together the vinegar, mustard and garlic in a medium bowl until combined. Slowly add the remaining 3/4 cup of olive oil and season with salt and pepper. Pour the vinaigrette over the potato mixture and mix gently to combine. Add the thyme and parsley and season with salt and pepper to taste. Serve at room temperature.