In a straight-sided ovenproof saute pan or skillet, heat the oil over medium-high heat. Season the pork with salt and pepper, dust with the flour, and cook in the oil until golden brown, about 2 minutes per side. Remove the meat and keep it warm.

Pour out all but 1 tablespoon of fat from the skillet. Add the onion and fennel; saute until they begin to soften, about 5 minutes. Add the garlic and fennel seed; saute briefly until both are fragrant. Season with salt and pepper. Add the wine, raise the heat, and boil until reduced to a syrup, scraping up the brown bits with a wooden spoon. Add the broth and boil until reduced to about 1/2 cup of liquid. Add the heavy cream and 2 cups of the milk. Simmer until the liquid is reduced by about half (you should end up with about 1-1/2 cups liquid).

Stir in the cabbage and potatoes and arrange the pork slices in the pan, adding any accumulated juices. Add another 1 cup milk. Turn the heat to medium low and cook gently, uncovered, adding more milk if needed to keep the pork just covered with liquid, lowering the heat if necessary, until the meat is fork-tender and the sauce is creamy, about 50 minutes. (Small milk curds may form in the sauce; this is okay.) If the sauce is too thick, add a little more milk to smooth it out.

Meanwhile, in a small skillet over medium heat, melt the butter. Fry the breadcrumbs in the melted butter until deep golden, tossing constantly. Add the chives to the breadcrumbs, sprinkle the mixture over the braise, and serve.