Ina Garten's Slow-Roasted Filet of Beef with Basil Parmesan Mayonnaise

INGREDIENTS

1/2 cup

Basil, fresh lightly packed Leaves

Branches fresh tarragon

1/2 tsp

Garlic

Egg yolks, Large

1 tbsp

Dijon mustard

3 tbsp

Lemon juice, freshly squeezed

2 tsp

Black pepper, coarsely ground

4 tsp

Kosher salt

Kosher salt and freshly ground black pepper

3 tbsp

Olive oil

1/2 cup

Olive oil, good

1 cup

Vegetable oil

1/2 cup

Parmesan cheese

Whole filet of beef tenderloin (trimmed and tied; 4 1/2 pounds)