Preheat oven to 400 degrees.
In a large Dutch oven, heat oil over medium-high heat until shimmering. Pat chicken dry and season with salt and pepper.
Working in batches, add chicken to Dutch oven skin-side down and brown until skin is golden and crispy. Turn and brown other side. Remove chicken and place in a 8x8- or 9x13-inch baking pan (depending on how much chicken you have.)
When finished browning the chicken, add shallots to Dutch oven and sauté until softened. Add wine to deglaze the pan, scraping any brown bits from the bottom of the pan. Reduce heat and simmer until most of the wine has evaporated.
Whisk in the chicken broth and whole grain mustard. Return to a simmer.
Pour sauce into the pan with the chicken, but do not pour directly on top of chicken. You want to keep the skin crispy. Braise the chicken, uncovered, in the oven for about 15 minutes or until cooked through.
Transfer the chicken to a platter and pour the sauce back into the Dutch oven.
Add smooth Dijon mustard and whisk to combine. Bring sauce to a simmer again reduce the sauce to your liking.
Remove from heat and add in heavy cream. Taste and season with additional salt and pepper if necessary.
Serve one of two ways: Either place some sauce in a shallow soup bowl and place chicken on top, or serve sauce in a small dish alongside chicken on a plate with other side dishes. Garnish with parsley if desired.