To prep the steak, pat very dry with paper towels and allow to sit at room temperature at least 10 minutes and up to 1 hour before cooking. Season generously all over with salt (about 1 ½ tsp.) and pepper (about 1 tsp.), including sides and ends. You’ll want to season the steak either more than 40 minutes (and up to overnight; chill in the fridge, uncovered on a rack, until ready to bring to room temperature) or less than 3 minutes before cooking.

To cook the potatoes, place them in a Saute Pan or Saucepan and add cold water just to cover. Cover with lid and bring to a boil over medium-high heat. Season generously with salt (about 1 Tbsp.), lower heat to medium, and cook potatoes, uncovered, until tender when pierced with a Paring Knife (but not mushy), 12–15 minutes. Drain.

Dry potatoes very well on a Sheet Pan lined with dish or paper towels. (This step can be completed up to 1 day ahead; chill until ready to use and bring to room temperature before continuing.)

Remove dish or paper towel from Sheet Pan, leaving potatoes behind. Use a lightly oiled Grill Press or the bottom of a small saucepan such as a Butter Warmer to gently smash the potatoes to a thickness of about ¾-inch, keeping them mostly intact. Strip the leaves off 4 thyme sprigs and set aside.

Wipe Saute Pan dry (or use a large Frying Pan) and heat over medium-high. Add olive oil and swirl to coat. Carefully add potatoes and sprinkle with ¼ tsp. salt and cook until crispy and golden brown on the underside, 4–6 minutes.

Gently flip potatoes, add thyme leaves and another ¼ tsp. salt, and cook until golden brown and crispy on both sides. Sprinkle ¼ cup grated Parmesan on top and remove from heat. Transfer to a paper towel-lined Sheet Pan or plate.

Meanwhile, cook the steak. Heat a seasoned medium Carbon Steel Frying Pan over medium-high until hot. Drizzle steak on all sides with neutral oil, then add steak to pan.

Cook steak, flipping every 2 minutes (don’t forget the sides and ends!), until a deep brown crust forms and the internal temperature reaches your desired doneness (120–125F for medium-rare). Depending on the thickness of your steak and the strength of your stovetop, searing should take 8–12 minutes. Set Frying Pan aside, reserving steak juices.

Rest steak on a cooling rack set over a Sheet Pan at least 10 minutes.

Return Frying Pan with steak juices to medium-high heat. Add 1 Tbsp. butter and allow to melt. Add mushrooms, ¼ tsp. salt, remaining 4 thyme sprigs, and cook until browned and softened, 4–5 minutes.

Cut remaining butter into 4 pieces. Add shallot to Frying Pan with 1 small piece butter; chill remaining butter. Cook, stirring, until shallots are softened, 1–2 minutes.

Measure stock in a liquid measuring cup, add mustard and Worcestershire, and whisk until smooth. Add stock mixture to pan and deglaze, scraping browned bits on the bottom of the pan with a wooden spoon. Bring to a boil, then reduce to a simmer and cook, stirring occasionally, until thickened and reduced by half, about 5 minutes.

Remove the pan from heat. Discard thyme sprigs. Add remaining pieces of cold butter one piece at a time, whisking with each addition. Taste sauce and adjust seasoning if necessary.

Slice steak against the grain, divide among plates, and drizzle with mushroom pan sauce.  Add potatoes alongside and top with remaining 1 Tbsp. Parmesan. Squeeze a little lemon juice over top (if using) and sprinkle with parsley, flaky salt, and freshly ground black pepper.