Add olive oil to a large, oven-safe skillet set over medium-high heat. Once the oil is shimmery and near smoking, place the fillets, peppercorn-side down, into the hot pan. Let fillets sear until golden-brown and crusty, about 4 minutes, then flip and sear on the other side, about 2 minutes.
Turn off heat under the skillet, then place the hot skillet in the oven to finish cooking the fillets. For medium, cook for 5 minutes, or until a meat thermometer inserted into the thickest part of the fillet reads 130F.
Remove skillet from oven and turn off the oven. Carefully transfer seared fillets to a plate. Wrap plate loosely with foil and place on the back of your stove so the beef can rest but stay warm.
Time to make the sauce! Place the same skillet over medium-high heat without cleaning it out. Add the minced shallots and stir to coat in the beef drippings. Let shallots cook down, stirring occasionally, until golden brown, about 5 minutes.
Add the red wine to the skillet and deglaze the pan, then let cook until the wine is mostly evaporated, 1-2 minutes.
Stir in the beef broth and bring to a simmer, then lower the heat and stir in the heavy cream, Dijon mustard, and thyme springs. Let mixture simmer into a silky sauce. Taste, then add any additional salt and pepper to your taste. Remove thyme sprigs before serving.
Serve Steak au Poivre sliced and covered with the cream sauce, or leave beef fillets whole over a puddle of cream sauce. Great with potatoes, rice, pasta, or polenta, or salad.