Place an 11- to 12-inch nonstick skillet over medium-high heat. Once hot, place the chicken sausages in the skillet and sear to warm through. Then move them to a plate and cover with foil.
Wipe the skillet out with a damp paper towel. Crack the eggs into a bowl, making sure you have 2 cups worth. Add 1/2 teaspoon salt and 1/4 teaspoon black pepper. Whisk throughly until the eggs are frothy.
Place 1 teaspoon butter into the skillet. Once melted, add 1/2 cup eggs. Swirl the pan to create an 11- to 12-inch even circle. Cook for 1-2 minutes until mostly cooked, then carefully flip the egg wrap over with a large spatula. Cook another 30-60 seconds. Slide the egg crepe onto a cutting board and repeat 3 more times, making 4 egg wraps total.
Lay each egg wraps flat and scoop half an avocado on the wrap. Spread the avocado into a thin layer. Then spread 2 tablespoons of jalapeño cream cheese over the avocado.
Place a chicken sausage on each egg wrap and fold the wrap over the sausage. Fold the sides inward, like a burrito, and roll the egg wrap, tucking the sides as you roll. Repeat.