Start by preparing the white wine vinaigrette. In a medium-sized mason jar, combine the white wine vinegar, dry yellow mustard, coarse salt, ground pepper, and extra-virgin olive oil. Secure the lid tightly and shake well until the ingredients are blended together. Adjust the seasonings to your taste.
Moving on to the broccolini tomato salad, begin by washing and halving the mini plum tomatoes. Place them in a serving bowl. Steam the broccolini until it is tender-crisp. You can then set it aside to cool or place it directly in a bowl of ice water to preserve its rich green color. Once the broccolini has cooled, roughly chop it into bite-size pieces. Add the broccolini to the serving bowl with the halved tomatoes. Toss the salad with the white wine vinaigrette and season with salt and pepper to taste.
Now it’s time to prepare the pan-seared chicken paillards. Butterfly each chicken breast by slicing it horizontally, or you can halve them if you prefer. Place each piece of chicken between two pieces of plastic wrap and pound them until they are evenly thin, about 1/4 inch thick. Season the chicken with salt and pepper.
In a skillet over medium to high heat, add 1 tablespoon of olive oil and 1 tablespoon of unsalted butter. Once the butter has melted and the skillet is hot, sear the chicken breasts on each side for approximately 1-3 minutes. Cook them until they are done and nicely golden brown.
To serve, arrange the pan-seared chicken paillards on a plate alongside the broccolini tomato salad. Drizzle any remaining white wine vinaigrette over the chicken and salad for an extra burst of flavor. You can garnish with fresh herbs like basil or parsley if desired.