Preheat the oven to 400°F (200°C). Line a baking sheet with parchment paper or aluminum foil.
Slice the bread lengthwise into two halves and place them cut-side up on the prepared baking sheet.
Heat a countertop griddle or skillet over medium and lightly spray or brush with olive oil.
Arrange the sliced red bell pepper on the griddle and cook until softened and slightly charred, then transfer to a small plate to cool.
Season the chicken breast with salt and pepper. If desired, slice the breast lengthwise for faster cooking. Grill or sear on the griddle until cooked through, then remove and let cool until safe to handle.
Place the grilled peppers in a food processor with 4 oz of the Greek yogurt and a pinch of salt and pepper; process until mostly smooth (some flecks are fine).
Spread the pepper-yogurt sauce evenly over both bread halves.
Slice or shred the cooked chicken and arrange it over the sauced bread.
Top the chicken with thin slices of tomato, then sprinkle evenly with the shredded 6-cheese Italian blend.
Bake in the preheated oven for 9 to 11 minutes, or until the cheese has melted and the bread is warmed through.
While the bread cools slightly, blend the remaining 4 oz of Greek yogurt with the minced garlic and a pinch of salt and pepper in a small food processor until smooth to make a garlic yogurt aioli.
Remove the baked bread to a cutting board, slice, garnish with chopped parsley if using, and serve with the garlic yogurt aioli on the side for dipping.
