TO PREPARE

1. Prepare the following, adding each to a large saucepan when complete: Peel 2 1/2 pounds russet potatoes and cut into 1-inch pieces. Add 2 large fresh sage sprigs and 1/4 cup of the heavy cream if using. Add enough cold water to cover the potatoes; do not cook yet.
2. Peel and slice 2 medium red onions into 1/4-inch rings and separate the rings
3. Heat 2 tablespoons unsalted butter and 1 tablespoon of the olive oil in a large cast-iron skillet or frying pan over medium heat until the butter is melted. Add the onions, 2 large fresh sage or thyme sprigs, and 1/2 teaspoon kosher salt. Cook, stirring occasionally, until the onions start to soften, 4 to 5 minutes. Add 1 tablespoon balsamic vinegar and 1 teaspoon granulated sugar and stir to combine. Cook, stirring occasionally, until the onions are caramelized, about 10 minutes.
4. After the onions have cooked for 10 minutes, add 1 1/2 teaspoons of the kosher salt to the saucepan with the potatoes. Bring to a boil over medium-high heat. Reduce the heat to maintain a simmer, and cook until the potatoes are tender, 15 to 25 minutes.
5. Meanwhile, carefully pour 1 cup dry red wine over the onions. Increase the heat to medium-high and boil for 2 minutes to let the alcohol burn off. Add 2 3/4 cups of the beef broth and 3 tablespoons Worcestershire sauce. Bring to a simmer, then reduce heat to medium and cook until the liquid has reduced by a third and the flavors meld, about 20 minutes. Cook the sausages while the sauce is simmering.
6. Heat the remaining 1 tablespoon olive oil in a second large frying pan or cast-iron skillet over medium-high heat until shimmering. Swirl to coat the bottom of the pan with oil. Add 8 uncooked sausages and cook, rolling them every few minutes, until evenly browned on all sides and cooked through (an internal temperature of 165ºF), about 12 minutes total. Transfer to a plate and cover with aluminum foil to keep warm.
7. When the potatoes are almost ready, microwave 3/4 cup whole milk with 4 tablespoons unsalted butter in a small microwave-safe bowl until the butter is melted and the milk is warm, 1 to 2 minutes. (Alternatively, simmer in a small saucepan over medium-low heat for 2 to 3 minutes.)
8. When the potatoes are ready, drain and discard the sage sprigs. Return the potatoes to the pot and cook over low heat for 2 minutes, stirring regularly (this dries out potatoes and yields a fluffier mash). Remove the pot from the heat.
9. Pour half of the warmed milk and butter and the remaining 2 tablespoons heavy cream if using over the potatoes and mash with a potato masher until potatoes have broken down and are fluffy. Add the remaining milk mixture in 2-tablespoon increments and use a fork to beat until smooth and creamy and the desired consistency is reached. Add the remaining 1 teaspoon kosher salt and 1/2 teaspoon ground white pepper or black pepper and stir to combine. Cover to keep warm.
10. When the gravy is ready, place the remaining 1/4 cup beef broth and 3 tablespoons cornstarch in a small bowl and stir until the cornstarch is suspended. Whisk the slurry into the gravy and simmer until thickened to the desired consistency, about 2 minutes. Add 1 tablespoon whole-grain or Dijon mustard and 1/2 teaspoon ground white or black pepper, and stir to combine. Discard the herb sprigs
11. Divide the potato mash between 4 large shallow bowls and place 2 sausages on top of each pile. Add any accumulated juices from the sausages to the gravy. Drizzle about 1/2 cup of the onions and gravy over the sausages on each plate. Pass the remaining onion gravy at the table