Adjust rack to middle position and preheat oven to 425 degrees. Wash and dry produce.

Cut potatoes into ½-inch-thick wedges. 

Toss potatoes on a baking sheet with a drizzle of oil, salt, and pepper. Roast on middle rack until browned and tender, 20-25 minutes.

Meanwhile, heat a large dry pan over medium-high heat. Add bacon*; cook, turning occasionally and adjusting heat if browning too quickly, until crispy, 6-10 minutes. Turn off heat; transfer to a paper-towel-lined plate.

Carefully discard all but a thin layer of bacon fat from pan. Reserve pan.

While bacon cooks, thinly slice mushrooms (skip if your mushrooms are pre-sliced!).

In a small bowl, combine horseradish sauce and mayonnaise.

Heat pan with reserved bacon fat over medium-high heat (if pan seems dry, add a drizzle of oil). Add mushrooms; cook, stirring occasionally, until browned and slightly crispy, 5-7 minutes. Season with salt and pepper.

Turn off heat; transfer mushrooms to a paper-towel-lined plate. Wipe out pan.

Arrange sourdough slices on a clean work surface. Evenly layer half the sourdough slices with gouda, bacon, mushrooms, and cheddar. Top with remaining sourdough slices to form sandwiches.

Heat 2 TBSP butter and a drizzle of oil in pan used for mushrooms over medium heat. Once hot, add sandwiches. (For 4 servings, work in batches; wipe out pan between batches and add more butter and oil as needed.) Cook, gently pressing down with a spatula or heavy-bottomed pan, until cheese slightly melts and bread is golden brown, 2-4 minutes. Add another 1 TBSP butter to pan, then flip sandwiches. Cook until cheese fully melts and bread is golden brown, 2-4 minutes more. TIP: Lower heat if sandwiches begin to brown too quickly. 

Halve sandwiches on a diagonal.

Divide sandwiches between plates. Serve with potato wedges and horseradish mayo on the side.