Combine the tomato paste, red wine vinegar, basil, garlic powder, sugar, salt, and pepper in a bowl or a blender. Whisk or blend until smooth.
Begin whisking in the olive oil, one tablespoon at a time, making sure it's fully incorporated before adding more. This allows the oil to emulsify into the tomato mixture, creating a smooth dressing. The dressing may separate slowly as it sits, but a quick whisk before drizzling over your salad will bring it back to a thick mixture.