Place 3 tbsp olive oil, the breadcrumbs, mustard, melted butter, 2 tbsp chives, and the chervil into a food processor. Season with salt and pepper and blend until thoroughly blended. Set aside.
In a large skillet heat one tbsp of oil and gently fry the onion, garlic, and bell peppers until the start to turn golden, about 3-5 minutes. Add the potatoes and cook for an additional 3-4 minutes.
Add the white wine and simmer until slightly reduced, stir in the cream and milk and bring to a slow simmer for about 3-4 minutes or until the potatoes are thoroughly cooked. Stir in 3 tbsps of chives and the mushrooms. Remove from heat.
In a large pan combine the herb and breadcrumb mixture, the creamy potato mixture and stir and add the beaten eggs, season well with salt and pepper.
In a separate non stick skillet add the remaining 2 tbsp of oil and fry the omelet mixture until it is golden brown on both sides, turning once. Remove from skillet, top with remaining chives and shredded cheese, serve at once.
