Heat 2 to 3 tablespoons of olive oil in a large skillet or sauté pan over medium heat. Add the chopped onion, minced garlic, and a pinch of red pepper flakes if you like a bit of heat. Cook, stirring occasionally, until the onions are translucent and the garlic is fragrant and softened, about 3 to 4 minutes.
Add the ground beef to the pan with the softened aromatics. Break up the meat using a wooden spoon or spatula and cook until the beef is nicely browned. Season with salt and black pepper to your taste.
Pour in the dry white wine and add the rosemary sprigs. Bring everything to a simmer, scraping up any browned bits from the bottom of the pan. Let the mixture simmer gently for about 5 minutes to allow the alcohol to reduce and the flavors to meld.
Stir in the sliced cremini mushrooms. Continue to cook, stirring occasionally, until the mushrooms are tender and have released some of their juices, around 5 to 7 minutes.
Pour in the beef broth and let the mixture cook for several more minutes, allowing the flavors to combine and the sauce to thicken slightly. This is a great time to taste and adjust the seasoning if needed.
Stir in chopped flat-leaf parsley and squeeze in the juice of half a lemon. Add the broccoli florets on top of the mixture, cover the pan, and cook for a few minutes until the broccoli just begins to soften.
Add the julienned sun-dried tomatoes to the pan. Cover and cook for an additional minute or two, just until the sun-dried tomatoes have softened and the broccoli is cooked to your liking. I like to keep the broccoli a bit crisp for added texture, but you can cook it softer if that's your preference.
If you'd like extra richness, stir 2 to 3 tablespoons of unsalted butter into the hot beef and vegetable mixture just before serving.
Serve the flavorful ground beef and vegetable mixture generously over a bed of cooked brown rice or egg noodles. Garnish with additional chopped parsley if you wish.