Preheat oven to 400°. Cut bread slices into 1/2-in. cubes. In a bowl, toss cubes with oil. Spread on a baking sheet, season with a pinch each of salt and pepper, and bake until crisp, 8 to 10 minutes.
In a bowl, whisk eggs with salt and pepper to taste. Heat 1/2 tbsp. butter in an 8-in. nonstick frying pan over medium heat until foam subsides. Pour half of eggs into pan and swirl to spread to edges of pan. Sprinkle with 1 tbsp. parsley and 1/2 tbsp. chives.
Lift edge of eggs with a heatproof flexible spatula and tilt pan to let uncooked egg flow underneath. Continue lifting edge and tilting pan, working your way around all sides, until eggs are just set and top is still a little moist, about 2 minutes total.
Sprinkle 1/4 cup cheese and 1/2 cup croutons over half of omelet. Loosen omelet with spatula. Tip pan to slide omelet, filled side first, onto a warmed plate; flip bare half over cheese as omelet leaves pan.
Make a second omelet the same way. Sprinkle remaining herbs over omelets just before serving.