Clean and dry the white button mushrooms, then remove the stems to create caps. Set aside.
In a small saucepan, melt 3 tablespoons salted butter and sauté the garlic for 1 minute. Whisk in the flour and cook for 2 minutes. Gradually stir in the half and half, then add the Parmesan cheese. Simmer until thickened and smooth. Remove from heat.
In a bowl, mix the breadcrumbs, melted butter, kosher salt, black pepper, grated white cheddar, and ¼ cup of the Alfredo sauce (reserve the rest for drizzling). Stir until well combined.
Spoon the filling into each mushroom cap, pressing gently to fill evenly.
Preheat the air fryer to 350°F (175°C) for 3–5 minutes. Lightly coat the basket with cooking spray and arrange the mushrooms in a single layer. Air fry for 8–10 minutes, until tender and golden brown on top.
Drizzle with the remaining Alfredo sauce and serve warm.