In a medium bowl stir together avocado, tomato, green onion, jalapeño, lime juice, and salt. Taste and add more lime juice and salt if needed.
Preheat the broiler and position a rack in the upper third of the oven.
In a large broiler-proof skillet melt butter over medium heat. Whisk in flour until smooth, then whisk in milk. Cook until bubbling. Take off heat and stir in mozzarella and pepper Jack. Stir until completely melted. If needed, briefly place skillet back on heat to melt cheese. Place skillet under the broiler and broil until bubbling and browned.
Serve warm topped with avocado salsa.