Bring a large sauté pan to medium-high heat and add 2 tablespoon olive oil. Place the cherry tomatoes face down and sear for about 5 minutes in the pan. The idea is to seal off the bottom of the tomatoes to keep in the juices, leaving you with a sweet and juicy bite later. Carefully remove from the pan and set aside.
Coat the chicken thighs in a thin layer of flour and season with salt and pepper.
In a large sauté pan at medium-high heat, add 2 more tablespoons of olive oil. Add the chicken and cook until browned on both sides. Set aside.
Add the halved shallots and cook for about 5-10 minutes until caramelized. Add the wine and mustard and stir to combine. Season with salt and pepper. Add the chicken and cook for about 15-20 minutes with the lid on.
Remove the lid and allow the sauce to thicken for another 10 minutes, or until the chicken is cooked through and the sauce is at the thickness that you prefer.
Add the cherry tomatoes back in and stir lightly to combine with the sauce. Lastly, add some torn fresh basil to the top and serve.