béarnaise sauce is a sauce of clarified butter thickened with egg yolks, seasoned with a shallot and vinegar reduction and, finally, tarragon. It is a robust sauce, often served with grilled steak or grilled fish of a substantial sort, like salmon. Larousse Gastronomique suggests that the sauce was first prepared in the 1830s by a chef named Collinet at his restaurant le Pavillon Henri IV outside Paris (Collinet was from the Béarn). However, the editors then point to a similar sauce spotted in a French recipe book of 1818.
