Prick the potatoes all over with a fork and brush them with 1 tablespoon of the melted butter. Put on a microwave-safe plate and microwave, flipping halfway, until fork-tender, 10 to 15 minutes. Set aside to cool slightly.
Meanwhile, preheat the oven to 450 degrees F. When the potatoes are cool enough to handle, cut into bite-size pieces and set aside.
Add the bacon to a sheet pan and bake until golden, about 15 minutes. Set the bacon aside on a paper towel-lined plate.
Add the potatoes, bell peppers and onions to the sheet pan and toss to coat in the bacon fat. Sprinkle with the garlic powder, paprika, 2 teaspoons salt and 1 teaspoon pepper and toss again to coat with the spices. Spread out in a single layer and bake, tossing halfway through, until the onions and peppers are softened, about 20 minutes.
Cut a 2-inch round from the center of each slice of toast; reserve the toast and rounds.
Push the vegetables aside on the sheet pan to make a space in one corner and arrange the toast in 2 rows in the empty corner. Spread the vegetables evenly around the toast and add the bacon on top of the vegetables.
Divide the remaining 1 tablespoon melted butter among the 4 holes in the toast and crack an egg into each. Place the 4 rounds around the toast. Bake until the eggs are set, 7 to 10 minutes. Top the eggs with chives and spread each toast round with butter.
Cutting the potatoes, peppers and onions the same size helps to ensure even cooking.
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