Preheat a gas grill to medium-high (400 degrees F to 450 degrees F (200 degrees C to 230 degrees C)) on 1 side, or push hot coals to 1 side of a charcoal grill. Place sausage links on the oiled grates over the unlit side of grill.

Cover and grill until a thermometer inserted into thickest portion of sausage registers 150 degrees F (66 degrees C), 8 to 10 minutes, turning halfway through cook time.

Move sausage to the lit side of grill; grill, uncovered, turning once halfway through, until browned and a thermometer inserted into thickest portion of sausage registers 160 degrees F (71 degrees C), 1 to 2 minutes. Serve as desired.

Preheat oven to 350 degrees F (175 degrees C). Line a large rimmed baking sheet with aluminum foil or parchment paper.

Arrange sausage links in an even layer, with at least 1-inch in between each link, on prepared baking sheet.

Bake in the preheated oven until a thermometer inserted into thickest portion registers 160 degrees F (71 degrees C), about 20 minutes. Serve as desired.

Place sausage links in an even layer, with at least 1-inch in between each link in a medium, high-sided skillet with about 1/4-inch water. Bring to a gentle simmer over medium-high, about 5 minutes.

Reduce heat to medium to maintain a simmer; cover and cook, undisturbed, until a thermometer inserted into thickest portion of sausage registers about 130 degrees F (54 degrees C), 6 to 8 minutes.

Increase heat to medium-high, uncover and cook, turning occasionally, until water is evaporated, sausages are brown, and a thermometer inserted into thickest portion of sausage registers 160 degrees F (71 degrees C), about 8 minutes. Serve as desired.