In a large pot, heat 2 tablespoons of extra virgin olive oil over medium heat. Season your choice of steak with salt and pepper, then add it to the pot, browning it for about 6-7 minutes or until nicely caramelized on all sides. Once browned, remove the steak from the pot and let it rest on a cutting board.

In the same pot, add diced onions and minced garlic, sautéing for 2-3 minutes until translucent. Stir frequently, scraping the flavorful brown bits.

Pour in 4 cups of beef stock and bring to a rapid boil over high heat. Add the cubed potatoes and reduce heat to medium-low. Allow to simmer for 10-12 minutes, or until the potatoes are fork-tender.

In a separate small pot, melt 3 tablespoons of butter over medium heat. Whisk in 1/4 cup of flour and cook for 1-2 minutes. Gradually whisk in 2 cups of milk until smooth.

Carefully stir the milk mixture into the pot with simmering potatoes, cooking for 3-4 minutes until the soup thickens and becomes creamy.

Slice the rested steak into bite-sized pieces, then add it back along with 1 cup of heavy cream. Heat through for 2-3 minutes.

Remove from heat and stir in 1 cup of shredded cheese until melted. Taste and adjust seasoning if necessary.

Ladle the soup into bowls and garnish with additional cheese and green onions before serving.