1. To prepare flans, rinse mussels with cold water; drain. Discard any broken or open shells that do not close when tapped on the counter. Set mussels aside.
2. Combine wine, shallots, and garlic in a large Dutch oven; bring to a simmer. Cook 1 minute. Add mussels to pan. Cover, increase heat to high, and cook 5 minutes or just until mussels open; discard any unopened shells. Remove from heat, and cool 5 minutes. Using a slotted spoon, remove mussels from pan, reserving cooking liquid. Remove meat from mussels; discard shells. Set aside.
3. Preheat oven to 350°.
4. Strain cooking liquid through a cheesecloth-lined sieve into a small saucepan; discard solids. Add saffron to cooking liquid; bring to a boil. Remove from heat. Add torn bread to saffron mixture. Let stand 5 minutes.
5. Set aside 6 mussels for garnish; chill. Pull off and discard rubbery rings from the remaining mussels. Combine mussels, saffron mixture, and cream in a food processor; process 1 minute or until smooth. Place eggs in a large bowl; stir with a whisk until just frothy. Add mussel mixture to eggs; stir until combined.
6. Cut parchment paper to fit in the bottom of each of 6 (6-ounce) ramekins. Line ramekins with parchment rounds; coat with cooking spray. Divide mussel mixture evenly among prepared ramekins. Place ramekins in a 13 x 9–inch baking pan lined with a dish towel (to anchor them in the pan). Pour boiling water halfway up the sides of ramekins. Bake at 350° for 20 minutes or until centers are just set. A slight wobble in the center is fine. Remove flans from pan; cool on a wire rack to room temperature.
7. To prepare dressing, combine vinegar, salt, and pepper in a small bowl. Gradually add 1 tablespoon oil at a time, stirring well with a whisk until each addition is incorporated and the dressing emulsifies and thickens slightly. Whisk in chives and tarragon.
8. Cut toasted bread into rounds using a cutter slightly larger than ramekins (or the rim of a clean, dry ramekin can be used). Working with one flan at a time, run a sharp knife around the edge of the flan and carefully invert onto a toast round; discard parchment. Set flan, toast side down, onto a small plate. Repeat with remaining flans and toast. Place 1 reserved mussel on top of each flan; drizzle each serving with 1 1/2 tablespoons dressing.