Preheat oven to 375 degrees. Butter the mini doughnut pan.
In a small bowl, whisk together eggs, milk, grated cheese and chives. Fill 6 doughnut cavities with egg mixture.
Roll 3 of the biscuit quarters into a rope and form into a circle to fill doughnut pan. Repeat with remaining dough. Brush with butter. Bake for 8 to 9 minutes.
Remove pan and cut each biscuit in half. Place an egg doughnut in between each half, along with a slice of tomato and some arugula.
