Put 1 tablespoon of the oil in a small skillet. Stir in the garlic and shallot and place over medium heat just until the garlic begins to sizzle. Remove from the heat and transfer the oil and garlic to a mini-food processor (or to a mixing bowl with a whisk). Add the remaining olive oil and the rest of the ingredients for the dressing and process until smooth and emulsified. Taste and season with more salt, pepper, vinegar as needed.
Make the salad
Sprinkle the chicken breasts with salt and the herbs de Provence. Cook the chicken on a medium-hot grill or in a 425 degree oven until the chicken is cooked through — about 5 minutes per side on a grill and 25 minutes in the oven.
Cook the pasta in boiling salted water until al dente. Drain and transfer to a serving bowl.
Add the beans, arugula and half the Dijon dressing to the pasta and gently toss. Slice the chicken and arrange on top of the salad. Drizzle with more dressing to taste and sprinkle with cheese.
The salad dressing and chicken can be made ahead of time, but I recommend cooking the pasta and then adding the dressing while it's still slightly warm for the best flavor.
I prefer to briefly cook the garlic and shallot to remove the raw bite in the dressing, but you can skip that step.