Make-Ahead: Bring 3 quarts water to a boil in a Dutch oven. Meanwhile, wash beans; trim ends, and remove strings. Set beans aside.
Cut off and discard 1/2" from each end of carrot. Using a vegetable peeler, cut 8 paper-thin lengthwise strips from carrot; trim ends evenly. Add carrot strips to boiling water in Dutch oven; cook 45 seconds or just until tender. Remove with a slotted spoon; set aside, and cool.
Return water to a boil, and add beans. Cook 5 minutes or until crisp-tender. Drain; rinse with cold water, and drain. Gather 8 to 12 cooked beans into a bundle; wrap 1 carrot strip around each bundle. Tie ends in a knot, or tuck ends under each bundle and place in a large baking dish.
Melt butter in a small skillet over medium heat. Stir in garlic powder, basil, and hot sauce; cook 30 seconds. Drizzle melted butter mixture over beans. Cover with aluminum foil, and chill up to 1 day.
When Ready to Serve: Bake beans, covered, at 350° for 10 minutes or until thoroughly heated. Sprinkle with pimiento, if desired, and lemon rind before serving. Serve carefully, keeping bundles wrapped with carrot strips.