BRATS: In a large saucepan, over medium heat, bring the beer to a simmer. Add the brats, and cook until plump, about 6 minutes. Set aside. Preheat the grill and start the potato salad.
POTATO SALAD: Place the potatoes in another saucepan, and cover them with salted water by 2-inches. Place the saucepan over medium heat, and simmer the potatoes until tender, about 15 minutes. Drain well, and return to the saucepan to keep warm.
Meanwhile, grab a skillet and cook the bacon until crispy over medium heat. Add the onions, and season with pepper. Sauté for 1 minute. Remove from the heat; set aside.
Transfer the potatoes and the bacon mixture (including the fat) to a large mixing bowl. Add vinegar (to taste), mustard, eggs if using, and green onions. Season with salt and pepper. Mix well. Using the back of a spoon, mash the mixture together.
Lightly brush the sausages with oil. Place on the preheated grill, and cook for a few minutes on each side, to give the sausages nice grill marks. Toast the rolls at the same time.
Remove the sausages from the grill, and serve on toasted rolls, with mustard and sauerkraut or grilled onions, alongside our warm potato salad.