Step 1Remove and discard skin from duck breasts. Remove tenderloins from undersides of each breast. Trim away any membranes, veins and cartilage. Trim ends of meat to form rectangular shape. Sprinkle underside of each breast with salt and pepper and grind five or six small slivers of allspice over each piece (a hand-crank or regular cheese grater will work if you don't have an allspice grinder).
Step 2Bring pot of heavily salted water to boil. Add cabbage and cook gently until tender, about 2 minutes. Remove to ice-water bath. Transfer to paper towels and pat dry.
Step 3Place leaf of cabbage on cutting board, with inside of leaf facing upward. Carefully cut large rib from leaf.
Step 4Tear off piece of plastic wrap about 20 inches long and lay it horizontally across work surface. Roll duck breast width-wise to form long cylinder. Place cylinder of duck in center of widest part of cabbage leaf. Trim leaf to length of breast, so leaf will easily wrap around roulade once. Roll up duck breast in leaf. Place roulade in center of bottom of sheet of plastic wrap. Roll up roulade in plastic, holding center, and rolling as tightly as possible.
Step 5Twist one end of plastic wrap several times against duck. This will secure shape of roulade. Repeat on other side, twisting in opposite direction. You should have perfectly shaped cylinder. Bring both ends of wrap over to center of roulade and tie excess in knot. Repeat with remaining breast and leaf. (These can be refrigerated for 2 to 3 days.)
Step 6When almost ready to serve, bring pot of water to boil, then reduce heat so water is just barely simmering, about 200 degrees. Place roulades in water and cook to internal temperature of 130 to 135 degrees, 7 to 10 minutes. Remove from water and let rest for 2 to 3 minutes.
Step 7While duck cooks, cook mushrooms and shallots in oil over medium-high heat, 5 minutes. Season with salt and pepper. When tender, add cream, bring to simmer and reduce by about 1/2 to sauce consistency, about 5 minutes. Stir in butter and remove from heat. Serve as is or, for a finer sauce, blend and strain.
Step 8Discard ends of each roulade if you like for better appearance, and slice roulades into three equal pieces. Discard plastic wrap. Serve on top of mushroom sauce.