Coarsely crumble the goat cheese. Toss with the grated carrot and season with salt and pepper.
Lay out a sheet of plastic wrap and spread the dill into a 12 by 4-inch rectangle in the center. Form the cheese mixture into a log in the center of the dill and roll up tightly, twisting the ends to seal. Refrigerate until firm, about 20 minutes.
Unwrap the log and transfer to a platter. Put the beet horseradish in a small bowl on the platter. Serve with the crostini or flatbread crisps.
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