In a small bowl, stir together the minced dill, lemon zest, grated garlic, and olive oil. Stir in salt and pepper to taste and set aside.

Heat the olive oil over medium heat in a 5 qt dutch oven. Add the sliced kielbasa and brown it, stirring occasionally for 7-8 minutes. Use a slotted spoon to transfer the sausage to a bowl.

Increase the heat to medium-high. Add the cabbage and stir to coat in the oil. Cook until pieces start to brown and soften, then add the onions and carrots. Cook for another 2-3 minutes until the onions soften.

Stir in the paprika, ground caraway, and dijon mustard. Pour in the chicken stock, add the sausage back in, and bring to a gentle simmer. Season with salt and pepper, cover, and simmer for 10 minutes.

While the soup simmers, melt the butter in a nonstick skillet over medium heat. Add the pierogies in a single layer and brown for 3-4 minutes. Flip them and brown for another 3-4 minutes. Remove from heat and set aside.

Remove the lid from the pot and add in the pierogies. Squeeze in the lemon, stir well, and season to taste with salt and pepper. Ladle the pierogi soup into bowls and drizzle with the dill oil.