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1
Begin by tying the filet mignon pieces: Lay the meat on a cutting board and wrap a piece of twine around the outside of each piece.
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2
Pull the twine tightly so that the meat is secure and tie a knot.
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3
Sprinkle both sides of the meat generously with salt and pepper.
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4
In a medium saute pan over high heat, add 2 tablespoons of the butter, the olive oil and garlic.
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5
When the butter begins to bubble, add the filet mignon pieces.
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6
Tip the pan slightly and baste the tops with the butter and olive oil.
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7
Cook until deeply browned, about 3 minutes, and then flip and continue cooking and basting on the other side.
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8
Next, turn the pieces on their sides and cook the edges until brown.
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9
Add the leeks and 2 tablespoons of the butter and saute until the leeks are soft, about 4 minutes; add the tarragon.
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10
Turn the heat to high and add the red wine.
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11
Let the sauce reduce by half, lower the heat to simmer and add the truffle oil.
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12
Place another saute pan on high heat.
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13
Spread the remaining 2 teaspoons butter onto the brioche halves and place in the pan until slightly browned, about 2 minutes.
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14
To serve, slice the filet mignon on the bias and place some slices onto one half of each brioche bun.
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15
Top with some sauce, leeks and the other half of each bun.
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16
Serve immediately.
