Pancake Breakfast Sandwich with Sausage and Avocado

Whisk together flour, baking powder, sugar, and salt in a bowl. Whisk together milk, egg, and butter in a separate bowl. Stir milk mixture into flour mixture until just blended and smooth. Let stand 15 minutes. Heat griddle or large nonstick skillet over medium heat; butter. Pour about 1/4 cup batter for each pancake on hot griddle. Cook until puffed, tops are covered with bubbles, and edges look dry, 3 to 4 minutes. Turn and cook until plump and cooked through, 2 to 3 minutes. Place pancakes in a single layer on a baking sheet, and keep warm in a 175 °F oven up to 30 minutes. Repeat with remaining batter. Wipe griddle clean with a paper towel and increase heat to medium-high. Cook sausage until no longer pink in the middle, 3 to 4 minutes per side. Top four pancakes with sausage, avocado, eggs, and arugula, dividing evenly. Top with remaining pancakes. Serve immediately.