Place the pork in a large bowl and add the brown sugar, sage, salt, garlic powder, smoked paprika, black pepper and red pepper flakes. Mix well using your hands. Form patties from heaping 1/4 cups of the mixture, about 1/3-inch thick.
Melt the butter in a large cast-iron skillet over medium-high heat. Cook the sausage patties in two batches until the internal temperature reaches 160 degrees F, about 5 minutes per side. Serve warm with eggs or pancakes. (See Cook's Note.)
Sausage patties can be cooked, cooled and then frozen. Thaw and reheat in the microwave, or on the stovetop in a skillet over medium heat.