Position a rack in the center of the oven and heat the oven to 425°F.
On a baking sheet, arrange the bread slices in a single layer and brush the top of each with olive oil. Bake until lightly browned, 7 to 8 minutes. While the toasts are still warm, rub the top of each slice lightly with a cut side of the garlic.
In a medium bowl, whisk the eggs, chives, 1/2 tsp. salt, and 1/4 tsp. pepper.
In a 12-inch nonstick skillet, melt the butter over medium heat. When the foam subsides, pour in the egg mixture and cook until the bottom just begins to set, 1 minute. Continue to cook, pushing the cooked portion of the eggs into the center of the skillet with a silicone spatula while tilting the skillet to let the uncooked egg run underneath, until no longer runny, about 1 minute more. Add the mascarpone and cook, stirring gently to incorporate, until the eggs are just set and very creamy, about 2 minutes; remove from the heat. Serve with the toast.