Preheat your oven to 400°F (200°C). Line a baking sheet or roasting pan with parchment paper for easy cleanup.
Place the beef sausages on the baking sheet. Drizzle with 1 tablespoon of olive oil and toss to coat. Arrange them in a single layer with space between each link.
Bake the sausages for 15 minutes. They should be starting to brown but not fully cooked yet.
While the sausages bake, melt the butter and remaining 1 tablespoon of olive oil in a skillet over medium heat. Add the sliced onions and a pinch of salt. Cook for 10-12 minutes, stirring frequently, until soft and starting to turn golden.
Stir the brown sugar, balsamic vinegar, and whole grain mustard into the onions. Simmer for 2-3 minutes until the mixture creates a thick, sticky syrup. If the glaze is too thick, stir in the beef broth.
Remove the sausages from the oven. Pour the sticky onion glaze over the sausages, tossing them gently on the tray to ensure they are well coated.
Return the tray to the oven and bake for another 10-15 minutes, or until the sausages are cooked through (internal temperature of 160°F/71°C) and the glaze is bubbly and sticky.
Garnish with fresh thyme and serve immediately, spooning any extra pan juices over the sausages.