Combine tomatoes, ½ teaspoon salt, and sugar in bowl and let sit for 30 minutes. Transfer tomatoes to fine mesh strainer and allow to drain. Return tomatoes to bowl along with 3 tablespoons oil, vinegar, and ¼ teaspoon pepper;toss to combine.
Adjust oven rack to about 4 inches from heating element and heat broiler; broil bread slices until golden brown on both sides. Brush both sides of each slice with oil and rub with garlic clove. Season with salt and pepper to taste.
In the food processor, puree ricotta, ½ teaspoon salt, and ¼ teaspoon pepper until smooth, about 1 minute. With processor running, slowly add remaining 3 tablespoons oil until incorporated. Spread ricotta mixture evenly on toast slices. Top toasts with tomato mixture and sprinkle with basil. Serve.