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1
For the steak, preheat a large saute pan over medium-high heat.
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2
Oil the rump steak and then place into the preheated pan.
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3
Cook for about 2 minutes on the first side, and then flip and finish cooking the second side, about 2 minutes more.
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4
This will yield a steak that is on the rare side; cook 1 to 2 minutes longer, per side, for a more well-done piece.
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5
Let rest for 5 to 10 minutes.
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6
For the Sauce Bearnaise, put the shallot, tarragon stalks, 1 tablespoon of the chopped tarragon and the chervil, if using, and the vinegar, wine, and peppercorns in a heavy-bottomed saucepan and boil until reduced to about 1 tablespoon.
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7
Don't move from the stove; this doesn't take long.
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8
Press the reduced liquid through a regular or tea strainer and leave to cool.
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9
Put egg yolks and water in the top of a double boiler.
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10
Set over the bottom, in which water has come to a simmer.
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11
Add the reduced and strained liquid and whisk well.
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12
Keep whisking as you add the butter, cube by cube, until it is all absorbed.
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13
Taste, season as you wish with the salt and pepper, and add lemon juice as you wish.
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14
Stir in the remaining tablespoon of fresh chopped tarragon as you're about to serve with the steak.
