Wrap tofu in several layers of paper towels and place on a cutting board. Place a cast iron skillet or other heavy object on top of the tofu and let drain 20 minutes. Crumble tofu into a bowl.
While tofu drains, heat a grill pan over medium heat. Brush sweet potato slices with 1 tablespoon olive oil. Grill 4 to 5 minutes per side or until tender.
Heat 1/2 tablespoon olive oil in a large skillet over medium-high heat. Add onion, carrot, garlic, and pepper to pan; cook 5 minutes. Add tofu, and cook 5 minutes longer.
Stir together tomato sauce, tomato paste, vinegar, Worcestershire sauce, brown sugar, and mustard in a bowl. Add tomato mixture and walnuts to pan, stirring to combine, and bring to a boil. Reduce heat to medium; simmer 8 to 10 minutes or until thickened, stirring occasionally.
Scoop tofu mixture onto a sweet potato slice, and top with another sweet potato slice to make a slider. Serve with a fork and knife.