Make the Lemon Pesto: Add the lemon zest, lemon juice, and basil pesto to a mixing bowl. Whisk until smooth and evenly combined.
Coat the Steak: Place the steak on a plate. Spoon part of the lemon-pesto mixture over both sides of the steak and spread it into an even coating. Reserve the remaining mixture for the pasta.
Heat the Skillet: Heat a large skillet over medium-high heat. Add the garlic herb butter and let it melt, swirling the skillet so the bottom is evenly coated.
Cook the Steak: Place the coated steak in the hot skillet. Cook for about 4 to 5 minutes per side for a steak about 1 inch thick, adjusting the time as needed for its thickness and your preferred doneness. The center should reach about 130°F for medium-rare or 140°F for medium.
Rest the Steak: Transfer the cooked steak to a cutting board. Let it rest for at least 5 minutes so the juices stay inside the meat.
Cook the Mushrooms: Add the sliced baby portabella mushrooms to the same skillet. Cook over medium-high heat for about 3 minutes, stirring occasionally, until they begin to soften and brown.
Toast the Garlic and Pecans: Add the minced garlic and chopped pecans to the mushrooms. Cook for 2 to 3 minutes, stirring frequently, until the garlic is fragrant and the pecans are lightly toasted.
Warm the Pasta: Heat the olive oil in a medium saucepan over medium heat. Add the fully cooked pasta and stir for 2 to 3 minutes, until heated through.
Add the Broth and Spinach: Pour the beef broth into the skillet with the mushrooms and pecans. Add the baby spinach and cook over medium heat for 2 to 3 minutes, stirring until the spinach wilts.
Combine the Pasta: Transfer the warmed pasta to the skillet. Add the reserved lemon-pesto mixture and gently toss until the pasta is evenly coated. Cook for about 2 minutes, or until the liquid lightly coats the pasta.
Slice the Steak: Slice the rested steak thinly across the grain to keep it tender.
Finish the Dish: Remove the skillet from the heat and gently fold in the sliced steak. Toss just long enough to combine and warm the meat without overcooking it. Serve immediately.