Preheat your oven to 170 degrees F, or the "keep warm" setting.
Pat the chicken dry and sprinkle both sides with salt and pepper (don't be shy!)
Sprinkle the flour over the chicken (or dredge it on a plate) to get them coated in flour.
In a large saucepan, heat 2 tablespoons olive oil over medium-high heat. Add the chicken, but don't crowd the pan; you want it to sear not steam. Do it in batches if your pan isn't big enough.
Sear the chicken for 4 minutes; flip and cook another 2-4 minutes, until cooked through. Add more oil to the pan before flipping if it is dry.
Transfer the chicken to a sheet pan or other oven safe dish and put it in the warm oven.
While the chicken is cooking, bring a medium pot of salted water to a rolling boil over high heat. (Add at least 2 teaspoons salt. It should taste like seawater.)
Prep the broccolini: trim about 1 and 1/2 inches from the bottom stems, and remove any leaves. Slice any larger pieces lengthwise so they are all a similar size.
When the water is boiling, add the broccolini all at once, cover with a lid, and set a timer for 2 minutes.
If the chicken is done and removed, add a tablespoon of oil to the hot pan over medium high heat. Transfer the broccolini from the water to the pan (careful! It will splatter). Saute for 1 minute, then remove to the pan of chicken in the oven. (If the broccolini is done before the chicken, don't leave it in the pot of water! It will get mushy. Transfer it to a bowl of cold water to stop the cooking process. Then saute as described.)
Add the shallots to the hot pan over medium high heat. (add a bit more oil if necessary) Saute for 2-3 minutes until soft.
Stir in the chicken broth and thyme sprigs. Bring to a boil and then simmer for 3 minutes. Stir in the cream and mustard. Simmer for 5-6 minutes, until the sauce has reduced and thickened some. Remove from heat and discard the thyme stems.
You can either add the warm chicken and broccolini to the pan or serve on a platter with the sauce over the top.
This would be great served with salad, bread, roasted potatoes, etc.