In a medium skillet, melt 1 T. of the butter. Add the shallot and cook over moderate heat until just beginning to brown.
Add the vermouth and cook until nearly evaporated, about 1 minute.
Remove from heat and stir in the cream cheese, crème fraiche, mayonnaise, mustard, chives and tarragon. Season lightly with salt and cayenne and scrape into a large bowl.
Stir in the crabmeat, breaking it up slightly with spoon. Spread the crab dip in a shallow baking dish or 12 shallow ramekins.
At this point, you can refrigerate overnight and return to room temperature before next step.
Preheat the broiler. Position a rack 10 inches from the heat.
In a small glass bowl, melt the remaining 3 T. of butter in the microwave on high heat.
Stir in the bread crumbs and a pinch of salt.
Sprinkle the crumbs over the crab dip and broil until the dip is heated through and the topping is golden. About 2 minutes – shift the baking dish for even browning.
Serve warm with pita chips or toasted baguette slices.