Special equipment: 1-inch circle cutter
Cut potato slices with a 1 to 1 1/2-inch circle cutter and soak in water to remove starch. Place on a rack placed over a shallow pan of water. Steam to al dente and set aside to cool. Using a melon baller (ball scoop) scoop out a recess in each disk.
Cook bacon and remove to paper towels to drain. Pour most of the bacon fat from the pan and add butter over medium heat. Add cabbage and season with black pepper. Cook until it begins to soften, about 10 minutes. Stir in corned beef, and crumble in bacon. Cook together for about 10 minutes to allow flavors to integrate, remove from heat and stir in horseradish.
Combine the milk, onion, bay leaf, cloves, and nutmeg over medium heat. Spoon the melted butter into a separate heat resistant bowl and whisk in the cornstarch, then whisk in 1/4 cup of the Parmesan, reserving the rest. When the milk is fairly hot, pour a small amount of it into the cheese mixture, stirring until the milk is thoroughly blended in. Return this to the remaining milk, and simmer for 15 minutes, stirring frequently. Remove saucepan from heat, season sauce to taste, with white pepper, and salt if needed. Remove and discard bay leaf and cloves. Immediately put a sheet of plastic wrap on top of the sauce to prevent a skin from forming.
Preheat oven to 400 degrees F.
Stir enough of the sauce and reserved Parmesan into the corned beef/cabbage mixture to bind into a thick mixture. Spoon the mixture onto prepared potato disks, sprinkle with Parmesan cheese and place on a baking sheet. Flash finish in oven until lightly browned, about 5 minutes (monitor to make sure they don't burn). Sprinkle with chives and serve.