Place nonstick skillet over medium-low heat. Add butter and let it melt. In a medium bowl, add eggs, and a little salt and pepper. Whisk until combined. Set aside. Once the butter is melted add the toast (you may have to do this in two batches, depending on the size of you skillet). Leave bread untouched until the bread turns golden brown on the bottom. Then remove from skillet and set on a serving plate, untoasted side down. Reduce heat in skillet to low.
Add eggs to nonstick skillet and leave undisturbed. Once the edge of the eggs starts to cook slightly, gently fold eggs over each other to cook the eggs more and prevent them from browning. Remove from heat right before the eggs finish cooking. Top eggs with slices of colby jack, one slice right next to the other. Cover the eggs until the cheese starts to melt.
Split eggs over two slices of brioche. Sprinkle with chives for garnish. Top with another slice of toasted brioche. Serve immediately.