Start the potatoes: Set a large deep 12-inch skillet with a lid on the stove. Put the potato chunks into the skillet and add enough cold water to cover them by about 1 inch.

Set the skillet over high heat. Add 1 teaspoon of the salt and bring the water to a boil.

Reduce the heat just enough to keep the water at a steady boil. Cook the potatoes for 12 to 15 minutes, until a knife slides through the center easily.

While the potatoes cook, finish any prep if needed. Keep the scallion whites and greens in separate small piles so they are easy to add at different times.

Drain the potatoes in a colander. Let them stand for 2 minutes so excess water can steam off.

Brown the sausages: Carefully wipe out the empty skillet and return it to the stove over medium-high heat. Add the olive oil.

Put the sausages into the skillet. Cook for 10 to 12 minutes, turning every few minutes, until they are browned on all sides and cooked through. Transfer the sausages to a plate.

Cook the cabbage: Lower the heat to medium. Add 2 tablespoons of the butter to the skillet.

Add the onion to the skillet. Cook for 3 minutes, stirring often, until it softens.

Add the sliced cabbage and 1/2 teaspoon of the salt to the skillet. Cook for 6 to 8 minutes, stirring now and then, until the cabbage is wilted, tender, and starting to brown at the edges.

Add the scallion whites to the skillet. Cook for 1 minute, stirring, until they smell fresh and mild. Transfer the cabbage mixture to a bowl.

Mash the colcannon: Return the skillet to low heat. Put the drained potatoes back into the skillet with the warm milk, Dijon mustard, the remaining 2 tablespoons butter, the remaining 1 teaspoon salt, and the black pepper.