Set the oven to 392°F (200°C/180°C fan) and cover a separate baking sheet with paper towels. The lined sheet will catch oil after the sausages finish their first roast.
Heat the sunflower oil in a large roasting pan in the oven for about 5 minutes. The oil should be very hot and ready to sizzle when the sausages touch it.
Carefully arrange the raw links across the hot pan in one layer and roast for 20 to 25 minutes, until browned and cooked through. Look for golden casings with browned patches, but don’t use color alone to judge doneness.
Lift the browned links onto the prepared baking sheet with a slotted spoon. The towels will absorb the surface oil that could otherwise loosen the glaze.
Empty the remaining fat into a heatproof container for disposal once cool, then carefully wipe excess oil from the roasting pan. The pan should no longer contain a visible pool of grease.
Blend the runny honey and mustard in a small bowl. Stir until no separate streaks of honey remain.
Place the drained sausages back in the roasting pan and turn them through the honey mustard mixture. Each link should carry a light, even coating.
Bake for another 5 minutes, giving the pan a careful shake halfway through and monitoring it closely. Remove the pan when the coating looks golden, glossy, and bubbling, before any patches scorch.
Combine mayonnaise with wholegrain or Dijon mustard to taste in a separate bowl while the sausages glaze. The dip should look creamy and evenly mixed.
Transfer the glazed links to a serving plate and bring them to the table immediately with the mustard mayonnaise. The coating should cling to the sausages rather than sit in a greasy puddle.