Step 1

For the barbecue sauce: Heat the oil in a medium saucepan over medium heat. Add in the onion, season with salt and pepper and cook until soft, about 5 minutes. Add in the garlic, chili powder, smoked paprika and cumin and cook for an additional minute to lightly brown the garlic and toast the spices.

Step 2

Carefully deglaze the pan with the lager or water, scraping any bits off the bottom. Stir in the ketchup, vinegar, brown sugar, mustard, molasses and soy or Worcestershire sauce and bring the mixture to a low boil. Reduce the heat to low, cover and simmer, stirring occasionally, for 35 minutes.

Step 3

For the mushrooms: Meanwhile, prepare a grill for high heat.

Step 4

In a large bowl, whisk together the oil, soy sauce, vinegar, honey, mustard, cumin and smoked paprika. Season with pepper. Toss in large pieces of the mushrooms to coat. Set aside to marinate while you prepare the slaw.

Step 5

For the slaw: Whisk together the mayonnaise, vinegar, granulated sugar and onion. Toss in the cabbage and carrot and season to taste with salt and pepper. Set aside.

Step 6

Lightly oil the grates of your grill and add the mushrooms. Press down with a spatula and cook the mushrooms until well charred and tender, 2 to 4 minutes per side. Remove the mushrooms to a bowl and, using 2 forks, pull the mushrooms into bite-size pieces. Pour over some or all the barbecue sauce and toss to combine.

Step 7

For serving: To build the sandwiches, divide the mushrooms over the buns and top with the slaw.