How to Make It
Bring a medium saucepan of salted water to a boil. Add the carrot, cover and simmer over moderate heat until tender, about 15 minutes. Drain, transfer to a mini processor and puree.
In the same saucepan, bring the wine to a boil. Ignite the wine and let the alcohol burn off. Add the shallot and boil over high heat until the wine is reduced by three-quarters, 8 minutes. Stir in the carrot puree and bring to a boil.
Remove the pan from the heat and whisk in the chilled butter, 1 tablespoon at a time, until the butter is incorporated and the sauce is smooth. Return the pan to low heat now and then to keep the sauce hot enough to melt the butter but do not let it boil. Season with salt and pepper; the sauce should be peppery.
Steaks, poached eggs, roast chicken.