• In two separate small saucepans, cook 1/4 cup dry barley and 1/2 cup dry rice according to the directions on the package (note that cooking times will vary depending on what type you choose to use.) Drain any excess water when done cooking. Add both cooked grains to a large bowl.
• While you're waiting for the grains to cook, continue prepping the other ingredients. Place 1 cup dry rolled oats in a medium bowl and cover with a couple of inches of cold water. Soak for at least 15 minutes. Drain using a fine-mesh strainer, pressing out any excess water with a spatula or spoon. Add to the bowl with the other grains.
• Wipe any visible dirt from 24 ounces mushrooms, break them into 1/2 to 1-inch pieces, and add the pieces to the bowl of your food processor. Pulse the food processor until the mushrooms are coarsely chopped (alternatively, do this by hand with a large chef's knife). Make sure not to overfill your food processor as this will make it difficult to get the mushrooms cut into uniform pieces. For a full-sized food processor, I recommend processing 24 ounces of mushrooms in 2-3 batches.
  
• Grate 1 medium onion using the large holes of a box grater.
• Heat 1 Tablespoon canola oil or neutral-flavored cooking oil in a large skillet over medium-high heat. Add the processed mushrooms, the grated onion, and half of the kosher salt to the skillet. Cook, stirring often, until all of the excess liquid has cooked off, about 15-20 minutes.
• Add the cooked mushroom mixture to the bowl with the grains. Stir in the remaining half of the kosher salt, 3 large eggs, 3/4 cup shredded mild cheese, 1/4 cup cornstarch, 2 cloves garlic, 1/2 teaspoon smoked paprika, and 1/2 teaspoon freshly ground black pepper. The mixture at this point will be quite wet and resemble thick oatmeal.
• Move oven racks to the lower-middle and upper-middle positions. Turn on the oven to 350°. Line two baking sheets with parchment paper.
• Decide how large you want your patties to be (I made mine all 1/3 pound or 151g, and this was just right for our appetites and buns. Anywhere from 1/4 pound to 1/2 pound would work). Use a measuring cup or kitchen scale to measure out portions for your patties. By hand or using a hamburger patty press, form the portions into patties of your desired size. Carefully place the patties onto a parchment-lined baking sheet.
  
• Bake the patties until they're fully set, about 30 minutes. If they're not set in the middle yet, place them back in the oven for about 5 more minutes. Larger patties may need a few extra minutes. At this point, they are safe to eat, but I recommend cooking them a second time to crisp and brown the edges. You could do this right away, or you could refrigerate or freeze the patties for later.
  

To crisp/warm the patties

• Right before serving, I recommend cooking the patties again to reheat/crisp and brown the edges. You can do this immediately after baking, from the fridge, or from frozen.
• In a skillet: heat a Tablespoon of oil in a skillet over medium-high heat. Add the patties and cover. Cook until the bottom of the patty is browned and crisp, about 5 minutes. Flip the patties and repeat on the second side.
• In an air-fryer: Brush or spray a very light layer of oil on both sides of the patties. Heat in your air-fryer until the outsides are crisp and the center is hot, about 10 minutes at 425°F.
• On the grill: Heat the grill on medium-high to high heat and clean the grates with a bristle-free grill scraper. Turn the heat down to medium and lightly oil the grates. Place your Mushroom Grain Veggie Burgers on the grill and cook until browned on the bottom, about 5-7 minutes. Flip the patties and repeat on the second side.