Preheat the oven to 400°F (200°C). Line a large sheet pan with parchment paper for easy cleanup.

Slice the sausage into 1/2-inch rounds. Peel and cube the sweet potatoes to 1/2-inch pieces. Trim the broccoli into similar-sized florets.

Spread the sausage, sweet potatoes, and broccoli in a single layer on the prepared pan. Leave small gaps between pieces so they roast instead of steam.

In a small saucepan, melt the butter or warm the olive oil over medium heat. Add the minced garlic and cook just until fragrant, about 30 seconds to 1 minute.

Stir in the honey, soy sauce or coconut aminos, and apple cider vinegar. Season with a pinch of salt and pepper. Bring to a gentle simmer and cook 2 to 3 minutes so the sauce slightly thickens.

Pour the sauce evenly over the sausage and vegetables on the sheet pan. Use a spatula or tongs to toss everything so all pieces are coated.

Roast for 25 to 30 minutes, stirring once halfway through. The sweet potatoes should be tender and the edges nicely caramelized. If pieces look ready earlier, check with a fork and remove when done.

Remove from the oven, sprinkle with minced parsley, and serve warm.