Steam mussels with wine and shallots in covered pot until they open. (Discard those that don't open.) Remove mussels from shells. Reserve. Strain liquid through double layer of wet cheesecloth into small saucepan. Reduce by boiling to 2T.
Saute garlic and chervil in olive oil over med heat for 2 minute Add fennel, lower heat slightly and saute until just limp. Add red peppers and heat through. Salt and pepper to taste. Add mussels; remove from heat and cover to keep warm.
Whisk 2 pieces of the butter into the wine reduction. Set over ow heat and whisk in remaining butter 1 piece at a time. Salt and pepper to taste. Set saucepan into larger pan containing hot water to keep butter sauce warm.
Meanwhile, cook tagliolini according to package directions. Drain and place in warm bowl. Toss with three-quarters of the butter sauce. Add mussel vegetable mixture and toss. Serve on warm plates with remaining butter sauce spooned over pasta. Garnish with chervil leaves.