In a large pot, place butter and lobster meat. On low heat, melt down butter and poach lobster just until cooked through, about 3-4 minutes. Remove tails and allow to cool aside. Pour remaining butter from the pot into a shallow bowl, and refrigerate for at least an hour or overnight, to solidify again.
Cube lobster tails into large chunks and place in a medium bowl. Add celery and onion, along with salt and pepper, and toss together.
In a small pot, cook on high heat the wine, vinegar, shallot, thyme, and W Sauce. Reduce to half, and strain. Add strained liquid back to cleaned out small pot, and add heavy cream. On low heat, bring to a simmer, and slowly add about ¼ cup of cold lobster butter and whisk until emulsified and creamy. Add white pepper and lemon juice.
Pour beurre blanc over lobster, and add chives and parsley. Toss together. Taste for seasoning and salt, if needed.
• In a medium skillet, turn heat to medium high, and butter brioche rolls. Add buttered sides of brioche to skillet and brown each side. Turn off heat and place rolls on a platter. Divide lobster and sauce amongst the 4 rolls. Serve immediately with celery leaf garnish.