Cut half of the asparagus into matchstick-sized strips. Bias-cut the remaining asparagus into 1-inch pieces.
In a large bowl combine the matchstick-cut asparagus, hash browns and salt. In a very large nonstick skillet, heat 2 tablespoons of the olive oil over medium-high heat. Add hash brown mixture to skillet and press top down with a spatula. Cook hash browns for 5 to 7 minutes without stirring. Invert onto a baking sheet and return to skillet, adding more oil as needed. Cook for 4 to 6 minutes more or until crispy and browned. Remove hash browns from skillet to a platter and top with American cheese slices; set aside.
In the same skillet heat remaining 1 tablespoon olive oil over medium-high heat. Cook remaining asparagus, sausage, sweet pepper, and onion for 5 minutes or until vegetables are tender, stirring occasionally. Remove from heat and stir in jalapenos, if desired. Cut hash browns into wedges and serve topped with sausage mixture.