Prepare the Chicken: Season the chicken tenderloins with salt and pepper, then lightly dredge them in flour, shaking off any excess. In a large skillet, heat 2-3 tablespoons of olive oil over medium-high heat. Sear the chicken for 3 to 4 minutes on each side, or until it develops a golden-brown crust and is fully cooked. Transfer the chicken to a plate and keep it aside.

Blanch the Broccolini: Fill a pot with salted water and bring it to a rolling boil. Add the broccolini and blanch for 2-3 minutes until bright green and tender-crisp. Drain the broccolini and set aside.

Prepare the Sauce: In the same skillet used for the chicken, add an additional tablespoon of olive oil if needed, then add the diced shallots. Sauté for 2-3 minutes until the shallots are softened and fragrant. Pour in the chicken broth and add the fresh thyme sprigs. Let the mixture simmer for 5-7 minutes until the broth reduces by half. Stir in the heavy cream and Dijon mustard, mixing well to create a smooth, creamy sauce. Allow it to simmer for an additional 3-4 minutes until slightly thickened.

Combine and Serve: Return the chicken to the skillet, along with the broccolini. Spoon some of the sauce over the chicken and broccolini to coat them evenly.