Preheat oven to 375°F. Split each raw biscuit in half. Arrange 12 halves in an even layer in bottom of a lightly greased 13- x 9-inch baking dish, and lightly press together. Bake in preheated oven until partially cooked and lightly golden, about 8 minutes. Reduce oven temperature to 350°F.
Top baked biscuits evenly with ham, and sprinkle with cheeses. Whisk together eggs, milk, mustard, salt, and pepper in a medium bowl until combined. Pour egg mixture evenly over ham and cheese.
Cut remaining biscuit halves in half, and line them along sides of baking dish. Cover with aluminum foil, and bake at 350°F until egg mixture is set, 45 to 50 minutes. Let stand 10 minutes. Sprinkle with chives, and drizzle with mustard.
Being a single person, I cut this recipe down to an 8x8 glass baking dish. Simple to make but I found the biscuits a bit “tough”. If I make it again, I may buy a different canned biscuit—flakier.