Heat Butter and oil in a skillet on medium. Add the onions and cook until translucent, about for 4 minutes, stirring occasionally. Add in half of the tomatoes and cook until fragrant, about 30 seconds.
Add the liquids: Add in the chicken broth and cream whisking constantly to combine. Bring to a simmer.
Add the chicken back to the pan along with the pasta. Bring to a slow boil, stirring occasionally, then immediately reduce to a simmer. Cover and cook for 10-15 minutes, or until the pasta is just al dente - Uncover the pan and stir once or twice during cooking to prevent the pasta from sticking together.
Reduce heat to low and stir in the parmesan cheese until melted. Taste and adjust for seasoning with salt and pepper. Add the ricotta and basil. Stir to combine. Garnish with more basil, parmesan.