Soak potatoes in cold water for 10 minutes, then drain well and pat dry.
Fill a 2-quart saucepan with 2 inches of water, add the vinegar, and bring to a slow simmer.
Heat 2 large nonstick skillets over medium heat, adding the olive oil to one of the skillets. Add the potatoes to the oiled skillet in one layer, being careful to spread them out. Season with salt and pepper, and brown for 5 minutes on each side, or until golden and crisp. Remove potatoes to serving plate, and cover to keep warm.
Meanwhile, in the second skillet, add the bacon, and cook until brown and crisp. Drain on paper towels, cut each piece in half, and cover with foil to keep warm.
Wipe out both skillets, and return them to the stove. Heat over medium. In the first skillet, cook the halloumi for 2 to 3 minutes per side, or until golden brown. Remove to a serving platter, and cover to keep warm.
Meanwhile, melt the butter in the second skillet, add the spinach, and stir to cover the spinach with butter. Cover, and remove from heat.
Return to the simmering water. Break the eggs into individual small ramekins or teacups, and gently slide each egg into the water. Turn off the heat, cover, and let sit for 5 minutes.
Assemble stacks on 4 individual plates in this order: a few potato slices, 2 slices of halloumi, 1 poached egg (use slotted spoon to remove from water), spinach, red pepper, and bacon. Garnish with black pepper to taste.