Preheat the oven to 325°F.
Mix grated cauliflower and carrots in a bowl with 1 tablespoon olive oil.
Spread on a baking sheet and roast in the oven for about 30–45 minutes, mixing occasionally, until softened and starting to brown.
While cauliflower and carrots are roasting, add 1 tablespoon olive oil to a sauté pan over medium heat.
Add diced onion and sauté for about 6 minutes, until translucent.
Add diced jalapeños and mushrooms and sauté for another 6–7 minutes.
Add garlic and sauté for another 2 minutes.
Remove from heat.
Once all vegetables have cooled slightly, combine with all other ingredients (except the remaining 1 tablespoon oil) in large mixing bowl. Incorporate all ingredients together with hands, and form 4 large patties. For a more solid veggie burger, refrigerate for 15–30 minutes before cooking.
In a large pan, add remaining tablespoon of olive oil over medium-high heat.
Add veggie burgers to pan and fry for about 6 minutes on both sides until browned.