In a Large pot or saucepan bring water to a boil on high heat adding a generous amount of salt. Add the pasta, stirring occasionally so as not to stick and cook according to suggested time on the box of the pasta less 2 minutes. Reserve ½ cup of cooking water.
Take a large saucepan and place on high heat. A minute later add the smashed garlic and the thyme. Sauté for 30 seconds and add in the tomatoes. Toss and sauté for 2 minutes and take off the fire. Discard both garlic and thyme sprigs and keep aside.
In the meantime, in a large and deep saucepan over low heat add the Pesto Genovese sauce and keep warm.
Strain the pasta and return to the saucepan with the pesto sauce. On low heat stir for a minute so as the pasta absorbs the sauce. Add from the reserved water if consistency is on the thick side.
Immediately add half of the cherry tomatoes and toss carefully not to brake the tomatoes.
Serve in a deep dish, add the Parmesan cheese and the rest of the cherry tomatoes. Finally, drizzle the rest of the oil.