Preheat oven to 350°F (175°C).

In a skillet, sauté diced onion and green pepper in a little olive oil until soft and caramelized, about 5–7 minutes.

Add shaved beef to the skillet and cook until just browned. Remove mixture from pan and set aside.

In the same skillet, melt the butter and whisk in flour to create a roux. Cook 1–2 minutes.

Slowly whisk in heavy cream and milk until smooth. Add Worcestershire sauce, salt, and pepper. Stir to combine and cook on medium low heat until slightly thickened.

Remove from heat and stir in cheddar, Monterey Jack, provolone, and cream cheese until melted and smooth.

Fold in the sautéed veggies and beef (if you want the pieces of beef to be smaller, I would chop up the mixture a little before adding it back to the pan).

Pour mixture into a baking dish. Top with extra cheese, if desired.

Bake at 350°F for 15–20 minutes, or until bubbly and golden on top.

Garnish with sliced scallions and a sprinkle of paprika. Serve warm with chips, bread, or veggies.