Trim and discard stem end and tough green top from leek; cut leek in half lengthwise and hold each half under cold running water, separating layers to rinse well, then thinly slice. In a 10- to 12-inch ovenproof nonstick frying pan over medium heat, melt 1 tablespoon butter. Add leek and stir often until limp, about 5 minutes. Transfer to a bowl.
Sort through crab and discard any bits of shell. Add remaining 2 tablespoons butter to pan; when melted, add crab and stir often just until hot, 1 to 2 minutes. Push to one side of pan.
Meanwhile, rinse salmon and pat dry. Holding a sharp knife at a 45° angle, cut flesh crosswise off the skin into 1/8- to 1/4-inch-thick slices; you should have about 12 (see notes). One at a time, lay slices flat and spoon about 1 tablespoon warm crab onto wide end. Starting at that end, roll salmon tightly around crab and place, seam down, in frying pan. Pour vermouth around rolls.
Transfer pan with salmon rolls to a 450º regular or convection oven and bake until fish is opaque but still moist-looking in center of thickest part (cut to test), 12 to 15 minutes. With a slotted spoon, transfer salmon rolls to plates, cover loosely with foil or plastic wrap, and let stand in a warm place.
Add cream and reserved leek to pan and boil over high heat until liquid is slightly thickened and reduced to about 1 1/3 cups, 8 to 9 minutes. Season to taste with salt and pepper. Spoon sauce equally around salmon rolls and garnish with chives and lemon wedges if desired.