If you have time, pound the chicken breasts to even thickness for quicker, more even cooking. If not, just pat dry and season well.
Brush the chicken lightly with olive oil and season with salt, pepper, and a pinch of garlic powder or oregano.
Grill the chicken over medium heat until fully cooked, about 6-7 minutes per side depending on thickness. Let rest a few minutes, then slice into thick strips.
While the chicken rests, lightly toast the bread halves on the grill or in a toaster oven until just golden.
Spread pesto on both cut sides of the bread. Layer with grilled chicken, roasted red peppers, and mozzarella slices.
Return the assembled sandwiches to the grill or oven just long enough for the cheese to melt and everything to warm through, about 2-3 minutes.
Cut in half and serve warm. If you like a little extra brightness, squeeze a tiny bit of lemon over the filling before closing the sandwich.