Season beef fillets with salt and pepper.

Trim tough ends of enoki mushroom stems.

Melt 1 tbsp butter in a small saucepan.

Add mushrooms and cook briefly (1 minute) until heated through. Remove from heat.

Heat oil in a heavy skillet.

Cook fillets for 3 minutes on one side.

Flip and cook for 2 minutes on the other side.

Transfer meat to a warm platter, drain fat from skillet.

Add 1 tbsp butter and shallots to the skillet.

Cook shallots for about 1 minute, stirring.

Deglaze with port wine and beef broth, scraping up browned bits.

Add Gorgonzola cheese and cook, stirring, until melted and sauce is reduced to 1/3 cup.

Strain the sauce through a sieve, pressing to extract all liquid.

Return sauce to saucepan and simmer, swirling in remaining 1 tbsp butter.

Spoon sauce over the fillets and garnish with mushrooms.