Cook the brown lentils according to the instructions on the package.
Make the rosemary fries: Preheat the oven to 475 degrees Fahrenheit. Line a baking sheet with parchment paper and put the potatoe wedges on top. Drizzle with olive oil and sprinkle with rosemary and salt. Bake for about 40 minutes or until crispy and brown.
Make the basil mayonnaise: In a food processor, combine the vegan mayonnaise and the basil leaves and process until smooth.
Put about 1/4 of the cooked lentils in a food processor together with the tofu, the mustard, the sun-dried tomatoes, and the tomato paste. Process until well combined.
In a small skillet, head the olive oil and sauté the onion for about 3 minutes or until it is translucent.
Add the remaining cooked lentils, the onion, the rolled oats, the whole wheat flour, the grated carrot, the spices, soy sauce, and mustard to the lentil-tofu mixture and stir well. Season with salt and pepper and form about 4 burger patties.
In a large pan, heat some olive oil and bake the patties for about 3 minutes on each side or until they are slightly brown.
Serve on buns with the basil mayonnaise, arugula, and tomatoes.