Heat a medium saucepan over medium heat. Add the oil and cook the onion and thyme until the onion is softened and translucent (about 5 minutes). Add the garlic and cook an additional 30 seconds or until aromatic.
Deglaze the pan with white wine. Simmer for about 2 minutes or until the wine has reduced by about half. Add the tomatoes and 1 ½ cups of water.
Simmer the soup for about 10 minutes, breaking up the tomatoes with a whisk, spoon, or kitchen scissors as they cook. Stir in 1 tsp. of the pesto. There should be 1 quart of soup. If not, add additional water.
Allow soup to cool before pureeing in a food processor or blender. Chill completely.
Once the soup is cold, taste and adjust seasoning.
Cook the stelline. Bring a small pot of salted water to a boil. Cook according to package directions. Drain and rinse under cold water. When the soup is cold, stir in the stelline.
In a small bowl, stir together the ricotta and remaining 1 tsp. pesto. Hold refrigerated until ready to serve.
To serve, divide the soup between 4 bowls. Spoon ¼ of the ricotta mixture into the middle each bowl and sprinkle 1 oz. of the chicken around it.