Preheat grill to high (or oven to broil).

In a saucepan, combine Worcestershire sauce with wine and cook over medium heat, stirring occasionally, until reduced to half, about 10 minutes. Add oil and remove from heat.

Meanwhile, cut potatoes into wedges and brush the mixture onto potatoes, using the sauce to generously cover them.

Spray broiling pan generously with oil. Place the potatoes on the broiling pan as evenly as possible, making sure that they don’t overlap too much. Sprinkle with a small amount of kosher salt, pepper and a generous amount of paprika.

Place the pan on the grill and close the cover. Let cook for about eight minutes.

Using a spatula, shuffle the potatoes in the pan and turn over as many as possible to make sure both sides cook evenly (it’s okay if you don’t get to each one). Close the lid again and let cook for about eight minutes more. Test readiness by sticking a fork into a large potato wedge to see how soft it is. (To broil in the oven, put under the broiler about four inches from the heat for about 12 minutes, mixing and turning them over halfway through cooking.)

Before you’re ready to eat, sprinkle potatoes with kosher salt one more time.