Cook pasta according to package, drain, and set aside.
In a large pot, heat the oil and butter over medium-high heat until melted.
Add carrots, onions, and celery to heated oil/butter. Stir frequently and cook until the onions become translucent. This will take about five minutes.
Stir in the garlic, pesto, and cook for another 2 minutes.
Add 8 cups of water and stir in the chicken stock base. Bring to a boil and lower heat. Allow to simmer for 10 minutes.
Add tomatoes and sugar to the pot and cover the pot. Simmer on low for 15 minutes. Adjust seasonings, if needed, by adding salt and pepper to taste.
Use an immersion blender to blend the soup until smooth. If you don't have an immersion blender, carefully transfer the soup to a blender in batches, and blend until smooth.
Gently stir in cooked pasta and serve warm.