Place the kielbasa on a cutting board. Using a sharp knife, make crosswise cuts about 1/4 inch apart, slicing three-quarters of the way through - stop before you hit the bottom so the sausage stays in one piece. A chopstick placed alongside the kielbasa helps prevent cutting all the way through.

Rub the kielbasa all over with olive oil, working some into the cuts. Transfer to a rimmed baking sheet, fanning the slices slightly so they open up.

In a small saucepan, combine mustard, honey, vinegar, and smoked paprika. Bring to a simmer over medium heat and cook for 2 minutes until slightly thickened. Remove from heat.

Roast the kielbasa at 400F for 15 minutes until it starts to render fat and the edges curl slightly.

Remove from oven and brush generously with about half the glaze, working it into the cuts. Return to oven for 8-10 more minutes until deeply browned and crispy at the edges.

Transfer to a cutting board or serving platter. Brush with remaining glaze and let rest 5 minutes. The cuts will open more as it rests, creating perfect sauce pockets.

Sprinkle with chopped parsley and serve warm. Provide bread for soaking up the glaze, or pair with buttered pierogies for a full meal.