Turn your grill on high to heat it up.Add the carrots and broccoli to a high speed blender or food processor and pulse/blend until everything is very finely chopped. Use the tamper tool for the blender and scrape under the blade as needed. In a large skillet over medium heat, warm the olive oil. Add the broccoli, carrots, and 1/2 teaspoon salt and cook until softened, about 3 minutes. Transfer to a large bowl to cool off.
Once the veggies are cool enough to handle, add the turkey, garlic powder, oregano, remaining ½ teaspoon salt, and pepper and mix to combine. Form into 4 large patties or 6 smaller ones. Drizzle oil onto each patty and rub around to coat on both sides (this will just help them brown better and not stick to the grill, but you can skip).
Grill the burgers for 3-5 minutes per side (covered), or until cooked through. Alternatively, cook them in a skillet over medium-high heat for about 3-5 minutes per side or until cooked through. Add a slice of cheese after flipping. Toast your buns on the grill or pan.
In a small bowl, mix together the yogurt, mustard, and salt. Spread Dijon yogurt onto the bottom bun and top with tomato, burger with cheese, avocado slices and top bun. Serve with pickles or chips, if you’d like!