Step 1

Boil the potato cubes with 2 cups of lightly salted water, until tender when you poke them with a sharp paring knife, about 10 to 15 minutes. Remove from heat and set aside.

Step 2

In a soup pot or Dutch oven, toast the caraway seeds over medium-high heat, stirring frequently, until they are fragrant and lightly toasted, about 3 minutes. Remove them onto a plate. (If you want to use some to garnish the finished soup, you can toast a few extra.)

Step 3

In the same soup pot, melt 2 tablespoons of the butter. Add the onion and cook, stirring frequently, until soft and translucent. Add the caraway seeds and cook for 1 minute more.

Step 4

Reserving about one-third of the cabbage (to sauté later), add half the rest of the shredded cabbage, 1 teaspoon of salt, freshly ground pepper, to the pot and stir everything together. Cover and lift the lid everyone once in a while to stir, until the cabbage wilts. You may need to add 1/4 cup (60ml) of water to the pot if it gets dry and starts to scorch on the bottom. (It wouldn't hurt to add another knob of butter here, either!) Once the cabbage in the pot is mostly wilted, add the remaining cabbage. (But don't use that reserved cabbage, which you'll be sautéeing later.) Cover and cook, stirring occasionally until all the cabbage is wilted.

Step 5

Turn off the heat and add the potatoes and their cooking water, and the milk to the pot. Use an immersion blender to blend the ingredients, or put them in a standard blender and puree until smooth, then pour back in the soup pot.

Step 6

Slice the reserved cabbage as thinly as possible. Heat the remaining 2 tablespoons of butter in a skillet, add the cabbage and season with a little salt and pepper. Cook, stirring occasionally until the cabbage is wilted. Add the sauteed cabbage the blended soup along with lemon juice or vinegar.

Step 7

To make the parsley oil, heat a small saucepan of water until boiling. Have a bowl of ice water handy. Plunge the parsley into the water and cook until wilted, 10 to 15 seconds. Remove it with tongs (or drain it), and immediately plunge the cooked parsley into the ice water, which'll guard its vibrant green color.

Step 8

When cool, squeeze as much water out of the parsley with your hands as you can and place it in a food processor or blender. The best option is if you have a mini-chopper food processor; this is a good place to use it! Puree the parsley with the oil until it's as fine as possible. Let stand for 1 or 2 hours. Place a square of muslin or a few layers of cheesecloth in a small mesh strainer set over a small bowl. Scrape the parsley and oil into the cheesecloth, then gather the ends and squeeze as firmly as possible - cheesecloth isn't as solid as muslin, go you may need to go easier on the pressure if using cheesecloth - to extract as much parsley oil as possible. You also put the mixture in a fine-mesh strainer and press it through that.