Preheat oven to 400 degrees F. Wrap garlic cloves in foil and roast 15 minutes, until golden brown and tender. Set aside.
Cook angel hair according to package directions.
Meanwhile, coat a stove-top grill pan or griddle with cooking spray and set over medium-high heat to preheat.
Season both sides of calamari with salt, black pepper and oregano. Place calamari on hot pan and cook 2 to 3 minutes per side, until browned.
In a blender, combine chicken broth and roasted garlic. Puree until blended. Transfer mixture to a saucepan and set pan over medium heat. Slice calamari into rings and add to simmering broth. Dissolve cornstarch in 1 tablespoon water and add to pan. Simmer 2 minutes, until sauce thickens. Drain pasta and transfer to a serving platter. Top with calamari and sauce. Sprinkle parsley over top just before serving.