Step 1Season the short ribs all over with 1 teaspoon salt.
Step 2Heat the oil in a large, heavy-bottom, lidded skillet over high heat until shimmering, about 1 to 2 minutes. Add the short ribs and sear until browned, 2 to 3 minutes per side. Add the carrot and onion to the pan and saute until tender and slightly browned, several minutes. Add the bay leaf, thyme and wine and bring to a simmer. Cook until the wine is reduced by two-thirds, about 10 minutes.
Step 3Add the veal stock and bring to a simmer. Return the short ribs to the braising liquid, cover the pan and bring to a gentle simmer. Braise the ribs, turning occasionally, until tender, about 4 hours, taking care to keep the liquid at a gentle simmer (not a boil).
Step 4While the ribs cook, place the cream in a small, heavy-bottomed sauce pan. Heat to a gentle simmer, and cook several minutes, stirring frequently, until the cream is reduced by half, taking care that the cream stays at a simmer and avoiding curdling or scorching. Remove from the heat. Stir in the mustard.
Step 5In a separate small pan over low to medium heat, bring the Cognac to a gentle simmer. Simmer until it is reduced to about 3 tablespoons. Stir it into the cream. Season to taste with salt. Reserve in a warm place until the short ribs are ready.
Step 6When the short ribs are tender, remove the meat from the braising liquid. Strain the braising liquid from the pan into a bowl or large measuring cup, then return it to the braising pan and bring it to a simmer over medium-high heat. Cook until the liquid thickens to a sauce consistency, several minutes. Return the short ribs to the pan and brush the meat lightly with the sauce to give it a shimmer. Remove the meat to a platter and serve with the mustard-cream sauce.