Season steaks generously on all surfaces with salt and pepper.
Add vegetable oil to 12-inch, heavy-bottomed cast iron or stainless steel skillet. Heat over high heat until oil just begins to smoke. Add steaks to pan and cook without moving until deep golden-brown crust develops on first side, three to four minutes. Flip steaks over.
Add butter, thyme sprigs, and shallots to pan. Turn heat down to medium-high. Continue to cook, occasionally basting steaks by tilting pan towards you and spooning hot fat over surface of steaks. If steaks start to become too dark, turn lower heat and rotate to all four sides. Continue to cook until instant-read thermometer inserted in to center of steak registers 115-125°F for rare to medium-rare.
Remove steaks from pan to a platter, pour juices, shallots and thyme from pan over steaks, tent loosely with aluminum foil and allow to rest for about ten minutes. Meanwhile, make pan sauce.
For the sauce: While steak is resting, Add shallot to pan and cook using pan's residual heat, stirring frequently, until softened, about 30 seconds. Add broth, wine, mustard and stir to combine. Simmer over high-heat until reduced to about 1/3 of a cup, 4 to 5 minutes. Remove pan from heat; whisk in parsley, butter, and lemon juice. Adjust seasoning.