1 In a food processor, coarsely chop the shallots (or onion) and garlic.
2 In a plastic or paper bag, combine the cornstarch, salt and 1/4 teaspoon of the pepper, and shake to mix. Add the chicken and shake to coat lightly. Remove the chicken and reserve the excess seasoned cornstarch.
3 In a large skillet, warm the butter in 1 tablespoon of the oil over medium-high heat until the butter is melted. Add the chicken and brown all over, 3 to 4 minutes per side. Remove the chicken to a plate and cover loosely to keep warm.
4 Add the remaining 1 tablespoon oil to the skillet. Add the shallot-garlic mixture to the skillet and cook, stirring, until light golden, 1 to 2 minutes.
5 Return the chicken (and any juices that have accumulated on the plate) to the skillet. Add the chicken broth, mustard, tarragon and the remaining 1/4 teaspoon pepper. Bring the mixture to a boil over medium-high heat.
6 In a small bowl, blend the cream and the reserved dredging mixture.
7 Stir the cream-cornstarch mixture into the skillet. Bring to a boil, stirring constantly. Reduce the heat to low, cover and simmer until the chicken is cooked through and the sauce is thickened, about 3 minutes.