Preheat oven to 400°F. Place a small rimmed baking sheet (about 17 x 12 inches) in oven 5 minutes. Remove pan from oven; brush with oil. Return to oven 2 additional minutes. Remove from oven, and arrange sausages on hot pan (making sure links do not touch). Bake until browned, about 15 minutes, turning sausages after 8 minutes. Transfer to a plate lined with paper towels; cool slightly, 5 minutes. Reserve 1 tablespoon drippings on pan. Reduce oven temperature to 325°F.

Chop sausages. Whisk together eggs and cream in a large bowl; stir in peppers, chives, salt, pepper, chopped sausages, and half of the cheese. Pour into pan with drippings; sprinkle with remaining 1 cup cheese.

Bake at 325°F until eggs are just set, 14 to 16 minutes. Cut into 32 squares. Spread mustard on bottom half of each biscuit, and then add 2 egg squares, arugula, sliced avocado, hot sauce, and biscuit top.