Cook sausage links according to package directions. Transfer to a cutting board and slice into 1-inch pieces; set aside.
In a medium saucepan over medium heat, gently stir together the beer and brown sugar. Bring to a boil for 1 minute, to dissolve the sugar, then reduce the heat to low. Simmer for 20 minutes, until the sauce reduces to about half its original volume. Whisk in the Dijon mustard and season with ground black pepper.
In a small bowl, whisk together the cornstarch and water, then pour the mixture into the sauce. Continue cooking, stirring frequently for 5 minutes, until the sauce is thickened.
Add the cooked sausage slices and gently stir to thoroughly coat with sauce. Serve hot.
Make-Ahead Option: These bratwurst bites can be made earlier in the day and kept warm in a slow cooker on the lowest setting.