Preheat the oven to 400°F. Line a large baking sheet with parchment paper.
Place the Italian bread cut side up on the baking sheet. Spread the softened butter evenly over both halves and sprinkle garlic salt across the surface. Bake for 8 to 10 minutes, or until lightly golden and crisp. Remove from the oven and set aside.
While the bread is baking, in a medium bowl, toss the chicken pieces with blackened seasoning until evenly coated.
In a large skillet over medium-high heat, heat olive oil until shimmering. Add the chicken and cook for 3 to 4 minutes per side, or until golden brown and fully cooked through. Transfer to a plate, tent loosely with foil.
In a separate saucepan over medium heat, melt the butter. Add the diced onion and cook for 3 to 4 minutes, or until translucent. Stir in the garlic and cook for 30 seconds.
Pour in the heavy cream and bring to a gentle simmer (do not boil). Stir in parmesan, salt, pepper, and crushed red pepper. Continue stirring until the cheese has melted and the sauce has thickened slightly, about 3 to 5 minutes. Remove from heat.
Spoon about ¾ cup Alfredo sauce over each toasted bread half, spreading to the edges. Reserve about ½ cup of sauce for serving.
Top with blackened chicken, then sprinkle with mozzarella and white cheddar cheese.
Return the bread to the oven and bake for 8 to 10 minutes, or until the cheese is melted and bubbly. For a more golden top, broil for 1 to 2 minutes, watching closely to prevent burning.
Let rest 2 to 3 minutes, garnish with parsley, slice, and serve warm with the reserved Alfredo sauce for dipping.