3 medium red or all-purpose potatoes (about 1¼ pounds), cooked, peeled if desired, and cut into ½-inch cubes (about 2½ cups)
3 medium beets (about 1¼ pounds), cooked, peeled, and cut into ½-inch cubes (about 2½ cups)
¾ pound cooked corned beef or roast beef, cut into ½-inch pieces (about 2½ cups)
Salt and pepper
1½ teaspoons yellow or spicy brown mustard
1/3 cup half-and-half
½ cup chopped fresh parsley
n In a large, heavy (preferably cast-iron) skillet, heat the oil over medium heat until it shimmers. Add the onions and cook, stirring frequently, until softened and golden, about 8 minutes. Add the thyme and garlic, stir to mix, and cook until fragrant, about 40 seconds.
Add the potatoes, beets, corned beef or roast beef, 1½ teaspoons salt, pepper to taste, mustard, and half-and-half, and stir to distribute.
Pat the mixture flat in the pan, and cook until moisture evaporates and the bottom begins to brown, 10 to 20 minutes. With a wooden spoon, stir the hash, scraping the bottom of the pan to loosen the crust. Stir to distribute the brown bits into the hash, flatten it in the pan again, adjust heat to medium-low, and continue to cook until a new crust begins to form, about 5 minutes. Again, scrape the bottom of the pan to loosen crust.
Add the parsley, stir to blend, taste the hash and adjust seasoning with salt and pepper, if necessary, and serve at once.