In a large bowl, combine duck breasts, ½ cup port, cane syrup, bay leaf, 1 tablespoon garlic, peppercorns, basil leaves, thyme, sage leaves, 2 teaspoons salt, and hot sauce. Toss well to fully coat meat with marinade. Refrigerate for 3 hours. Let stand at room temperature for 1 hour.
Heat a large cast-iron skillet over medium-high heat. Remove duck breasts from marinade, and pat dry. Add to pan, skin side down, and cook until light brown. Continue cooking, turning occasionally, until a meat thermometer inserted in thickest portion registers 165°. Remove, and keep warm, reserving 1 tablespoon drippings in pan.
Add shallot and remaining ½ tablespoon garlic to pan; cook for 2 minutes. Add blackberries and remaining ¼ cup port; cook until reduced by half. Add demi-glace; cook until reduced by a quarter. Season to taste with salt and pepper.
Slice duck breasts. To serving plates, add a generous portion of blackberry sauce. Top with duck, and garnish with micro greens, if desired.
Recipe by Louisiana Cookin' at https://louisianacookin.com/breast-duck-blackberry-demi-glace/