Julienne each of the Bell Peppers into thin slices. Place into a baking pan and roast peppers under an open broiler until skin begins to brown about 5 - 10 minutes. Remove from broiler and let cool.
Spread a thin layer of Mayo on the inside of each slice of rye bread. Mix olive oil and basil together in a small dish. Brush the opposite side of 5 bread slices with the Basil/Olive Oil mixture.
Place the 5 slices of bread onto a preheated griddle with the Olive Oil side down. Layer 3 slices of roast beef on top of each slice of bread. Place Roasted Peppers over the beef. Top with 2 slices of Baby Swiss Cheese.
Place other other 5 slices of rye bread on top of the cheese with the mayo side down. Brush the top sides with Basil/Olive Oil mix.
Grill until cheese is melted and sandwich is golden brown on both sides. Cut each sandwich in half to serve.
Side dish suggestion (Eggplant Steak Fries with Marinara Sauce).