Heat 3 tablespoons oil in a large saucepan over medium-high. Add onion and garlic; cook 5 minutes, stirring frequently, until softened. Add tomato paste; cook 1 minute, stirring constantly. Remove from heat; stir in 2 1/2 pounds chopped tomatoes, stock, salt, pepper, and 1/2 cup basil.
Transfer half of tomato mixture to a blender. Process 1 minute or until smooth. Pour pureed tomato mixture into a bowl. Transfer remaining tomato mixture to blender; process 1 minute or until smooth. With blender running, add 1/4 cup oil in a slow, steady stream, processing until smooth. If freezing, follow freezing instructions. If using immediately, add tofu to tomato mixture in blender; process until smooth.
Return pureed tomato mixture and pureed tomato-tofu mixture to pan; bring to a simmer, and cook, stirring often, until heated through.
Combine heirloom tomatoes, corn, vinegar, and remaining 1/2 cup basil in a bowl. Divide soup evenly among 8 bowls. Top with corn mixture; drizzle remaining 1/4 cup olive oil evenly over top.
How-To: FREEZE: Combine pureed tomato mixtures. Freeze in a large ziplock plastic freezer bag up to 2 months. THAW: Microwave soup in freezer bag on MEDIUM (50% power) 8 minutes or until thawed. REHEAT: Place half of soup in a blender. Add tofu; process until smooth. Combine with remaining soup in a saucepan; simmer until heated through. Proceed with step 4.