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1
Light a grill or heat a grill pan.
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2
Season the steak with salt and pepper and grill over high heat, just until nicely charred outside and raw within, about 1 1/2 minutes per side.
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3
Let the steak cool, then refrigerate until thoroughly chilled, about 1 hour.
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4
Meanwhile, in a small saucepan, combine the wine vinegar with half of the minced shallots and boil over high heat until the vinegar is reduced to 1 tablespoon, about 3 minutes.
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5
Transfer the reduction to a small stainless steel bowl.
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6
In a small saucepan, bring 1/2 inch of water to a boil; keep the water simmering over low heat.
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7
Add the egg yolks to the vinegar reduction and whisk over the simmering water until the mixture is thick, about 1 minute; if the egg sticks to the sides, remove the bowl from the simmering water to prevent overcooking the yolks.
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8
Remove the bowl from the simmering water and gradually whisk in the melted butter.
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9
Stir in the chopped tarragon and season with salt and pepper.
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10
Trim the fat and silver skin from the steak.
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11
Chop the meat very finely and transfer to a bowl; alternatively, pass the meat through a meat grinder.
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12
Stir in the parsley, chives, olive oil and the remaining shallots; season lightly with salt and pepper.
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13
Mound the steak tartare in the center of each plate.
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14
Carefully reheat the bearnaise sauce over the pan of simmering water, whisking constantly.
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15
Spoon the bearnaise sauce over the steak tartare and serve right away, with potato chips.
