Stir yogurt and basil together in a bowl; place in refrigerator.
Heat a large skillet over medium-high heat, and cook and stir beef until browned and crumbly, 5 to 7 minutes; drain and discard grease. Stir water and taco seasoning into beef; bring to a boil. Reduce heat to low; simmer beef mixture until thickened, about 5 minutes.
Spoon about 1 tablespoon yogurt mixture into each taco shell; layer in beef mixture, mozzarella cheese, cucumber, carrots, and a few strips of sun-dried tomato. Top with hot sauce and remaining yogurt.