Season your rump steaks generously with salt and pepper on both sides. Heat olive oil in a large skillet over high heat until it shimmers. Add the steaks and cook for 3-4 minutes per side, undisturbed, until a deep brown crust forms.
Add butter, chopped garlic, and the rosemary sprig straight into the pan with the steaks. Tilt the pan and spoon the melted, garlicky butter over the steaks as they finish cooking to your preferred doneness. Remove the steaks and let them rest for 5 minutes before slicing thinly.
While the steak rests, bring a large pot of salted water to a rolling boil. Cook the pasta according to the package directions until al dente. Before draining, scoop out 1-2 cups of starchy pasta water and set it aside for the sauce.
Using the same skillet you cooked the steak in (scraping up those flavorful browned bits), melt more butter over medium-low heat. This reuses all the leftover steak flavor instead of wasting it.
Add the remaining chopped garlic and cook for about 1 minute, just until fragrant. Stir in the Italian seasoning, then pour in the chicken stock and let it simmer for 1-2 minutes to build a flavorful base.
Pour in the heavy cream and let the sauce simmer gently for a couple of minutes until it starts to thicken slightly. Keep the heat moderate so the cream doesn't scorch or separate.
Add the cooked pasta and sliced steak into the sauce, then stir in the freshly grated Parmesan until it melts and coats every piece. If the sauce looks too thick or dry, splash in a little of the reserved pasta water to loosen it.
Fold in the chopped parsley and adjust the seasoning with more salt and pepper if needed. Serve the pasta right away while it's hot, topped with a little extra Parmesan if you're feeling generous.