Toast walnuts on center rack of 350F oven for 8-10 minutes, until toasted and fragrant.
Heat 1 tbsp oil in skillet over medium heat. Add mushrooms, garlic, shallot, roasted peppers, and ½ tsp salt. Cook until mushrooms brown, shallot softens, and liquids have cooled off, 6-8 minutes.
Add to food processor and process with other ingredients.
Scoop burgers with ½ cup measuring cup to make Pattie’s and fry.