Gently saute the shallot in the butter until translucent. Add the wine and reduce by half. Add demi-glace, tomato puree, chicken stock, garlic, herb stems, and half of the ham. Gently simmer for 30 minutes. Strain through a fine mesh sieve or a piece of cheesecloth. Stir in the remaining ham, horseradish, and parsley and spoon alongside red meats.