Bring a large pot of well-salted water to a rolling boil. Cook pasta according to package directions until al dente. If using broccoli, add florets during the last 2-3 minutes of cooking. Reserve 1/2 cup pasta water before draining. Drain pasta and broccoli together and set aside.

While pasta cooks, whisk together honey, soy sauce, minced garlic, rice vinegar, sriracha (if using), and ground ginger in a small bowl until thoroughly combined and smooth.

Heat olive oil in a large skillet over medium-high heat. Add sausage rounds in a single layer and let sit undisturbed for 2-3 minutes until caramelized on the bottom. Flip and cook another 2-3 minutes until both sides are golden brown with darker edges.

Pour prepared honey garlic sauce over the browned sausage. Let simmer for 2-3 minutes, stirring occasionally, as the sauce reduces and thickens into a sticky glaze that coats the sausage.

Add drained pasta and broccoli to the skillet with glazed sausage. Toss thoroughly using tongs or a large spoon to coat everything in the sticky sauce.

Let everything cook together for 1-2 minutes, tossing occasionally, allowing pasta to absorb sauce and flavors to meld. If sauce seems too thick, add reserved pasta water a tablespoon at a time to loosen.

Remove from heat and garnish generously with sliced green onions and sesame seeds. Serve immediately while hot and sauce is at its stickiest.