Step 1Combine the shallots, peppercorns, dried tarragon and vinegar. Reduce until almost all the liquid is gone, about 3 to 5 minutes.
Step 2Add the wine and water to the reduction; strain.
Step 3Combine the strained reduction and the egg yolks in a stainless steel bowl. Whisk the mixture in the bowl placed over a pan of hot water until the yolks are warm. To prevent overcooking, keep the bowl from touching the hot water.
Step 4Drizzle the clarified butter in a thin stream into the yolk mixture, whipping constantly. Add the chopped tarragon and chervil to complete the bearnaise.
Step 5Whisk the bearnaise into the demi-glace. Adjust the seasoning. Serve immediately.