Preheat your oven to 400°F (200°C).
Line a sheet pan with parchment paper or lightly coat it with nonstick spray.
Arrange sliced sausage, diced sweet potatoes, and broccoli florets in an even layer on the prepared sheet pan.
In a small saucepan over medium heat, melt unsalted butter before adding minced garlic. Sauté until fragrant, then stir in honey, low-sodium soy sauce, apple cider vinegar, salt, and black pepper, simmering briefly to meld flavors.
Pour the honey garlic glaze over the arranged sausage and vegetables on the sheet pan. Toss everything together until fully coated.
Place your sheet pan in the preheated oven and roast for about 25–30 minutes, stirring halfway through cooking.