Preheat the oven to 375°F.
Season the chicken breasts with salt and pepper. Dredge each breast in flour, dip in beaten eggs, and coat with breadcrumbs.
Heat olive oil in a large skillet over medium heat. Cook the chicken for about 5-6 minutes on each side until golden brown and cooked through. Remove and place on a baking sheet.
In a small saucepan, combine marinara sauce and red pepper flakes. Heat over low until warmed through.
Top each chicken breast with a generous spoonful of marinara sauce and a piece of burrata cheese. Bake in the oven for about 10 minutes, or until the cheese is melted and bubbly.
While the chicken is baking, melt butter in the same skillet over medium heat. Add sliced onions and cook, stirring occasionally, for about 15-20 minutes until caramelized.
For the chimichurri, combine parsley, oregano, red wine vinegar, olive oil, salt, and pepper in a bowl. Mix well.
To assemble the sandwiches, place a piece of chicken on each hoagie roll, top with caramelized onions, and drizzle with chimichurri. Sprinkle with grated Parmesan cheese.
Serve immediately and enjoy!