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

Cut potatoes into ½-inch-thick wedges. Halve, peel, and thinly slice onion.

Toss potatoes on a baking sheet with a drizzle of oil, salt, and pepper. Roast until browned and tender, 20-25 minutes. TIP: If you added any other items to your meal (apps, sides, and/or dessert), you can get started on them now!

Heat a drizzle of oil in a large, preferably nonstick, pan over medium heat. Add onion, salt, and pepper. Cook, stirring occasionally, until softened and lightly browned, 8-10 minutes.

Add ¼ cup water and 1 tsp sugar to pan with onion (⅓ cup water and 2 tsp sugar for 4 servings). Cook, stirring, until caramelized and jammy, 2-3 minutes more.

Turn off heat; transfer to a small serving bowl. Wash out pan.

Meanwhile, using the tip of a spoon, remove and discard black gills from undersides of mushrooms; trim any large stems if necessary. Halve mushrooms; thinly slice crosswise.

Heat a large drizzle of oil in pan used for onion over medium-high heat. Add mushrooms, garlic powder, and half the thyme (all for 4 servings); season with salt and pepper. Cook, stirring, until browned and tender, 5-7 minutes. Turn off heat; transfer to a second small serving bowl. Wipe out pan.

While mushrooms cook, thinly slice tomato. Transfer to a plate; season all over with salt and pepper.

Place mozzarella, cheddar, and dressing in separate serving bowls. Arrange family style along with jammy onion, garlic mushrooms, tomato, and sourdough for everyone to build their own sandwiches. (You’ll cook the sandwiches in the next step!)

Heat 2 TBSP butter in pan used for mushrooms over medium heat. Add sandwiches to hot pan (for 4 servings, you may need to work in batches, adding more butter between batches). Cook, covered, until bread is golden and butter is absorbed, 2-4 minutes. TIP: Lower heat if browning too quickly.

Reduce heat to medium low. Flip sandwiches, adding an additional 1 TBSP butter to pan. Cook, covered, until bread is golden and cheese melts, 2-4 minutes more.

Halve sandwiches on a diagonal. Serve with potato wedges and any remaining dressing on the side for dipping. (Don't forget to serve with any extra items you may have ordered to build out your meal!)