To prepare the soup, heat olive oil and butter in a heavy bottom pot and sweat shallots, fennel, black peppercorns, saffron, Piment d’Espelette and coriander over medium heat until vegetables have softened. Deglaze with white wine and Sherry. Increase heat to high, add mussels and steam until mussels have opened (6-8 minutes). Remove mussels from liquid and refrigerate. To the pot, add mussel stock and heavy cream. Reduce by one-third. If not using immediately, rapidly cool and refrigerate for up to 48 hours (soup will reheat nicely).
Bring a pot of seasoned water to a rapid boil and blanch carrots until just cooked through (3-4 minutes). Spoon carrots onto a small plate and reserve. Blanch salsify in same water (6-8 minutes) and reserve with carrots. Melt butter in a large cast iron skillet over medium heat. To the butter, add olive oil, soy sauce, honey, fennel powder, cumin and salt to taste. When foam subsides, add vegetables and sauté to color and glaze (2-3 minutes). Season to taste and reserve.
In a pot over low heat, gently warm billi bi soup. Spoon vegetables into six small, warm bowls and lightly coat with a thin, even layer of soup. Garnish with caviar and chervil.