Make the wild boar–mushroom patties: preheat the oven to 350°F. In a food processor, add both types of mushrooms and pulse until they are chopped. Place the chopped mushrooms in a medium mixing bowl and add the chopped garlic, chopped ginger, tamari, sugar, pepper, and salt and mix well. Add the mushroom mixture to a baking tray and gently press down to flatten it. Place the tray in the oven and cook, stirring the mixture every 10 minutes, until the mushrooms are dark brown, about 20 minutes. Remove from the oven and let cool completely.

In a large bowl, combine the cooked mushroom mixture with ground wild boar. Weigh into 5-ounce portions and gently form into patties.

Make the fried mustard greens: in a large Dutch oven, preheat the grapeseed oil to 350°F. Pat the mustard greens dry and tear into large pieces. Working in batches, carefully place the greens into the hot oil and fry until they’re crispy, about 1 minute. Drain the greens on a tray lined with paper towels.

Make the Sriracha vinaigrette: add the Sriracha and rice wine vinegar to a sealed container and shake vigorously until emulsified.

Cook the burgers: heat a well-oiled cast-iron skillet over medium-high heat. Cook the patties until they’re seared on one side, about 3 minutes. Flip and repeat until seared on the other side, about 3 minutes.

To serve: spread a thin layer of mayonnaise on the bottom of the brioche bun. Top with the burger, pickled red onions, and fried mustard greens. Dress with the Sriracha vinaigrette and top with the other half of the brioche bun.