In a medium saucepan, bring the parsnips, chicken broth, half-and-half and 1 tablespoon butter to a simmer over medium heat. Cook until the parsnips are tender, about 15 minutes. Transfer to a food processor and puree; season with salt and pepper. Keep covered.
Meanwhile, in a medium bowl, combine the flour with 1/2 teaspoon each salt and pepper. Add the okra and toss to coat. In a large skillet, melt the remaining 1 tablespoon butter over medium heat. Add the okra and cook, turning occasionally, until browned and crisp, about 5 minutes; drain on paper towels.
In the same skillet, add the lamb and garlic and cook over medium heat, breaking up the meat, until no longer pink, about 2 minutes. Stir in the diced tomatoes and simmer until slightly thickened, about 5 minutes. Stir in the okra; season with salt and pepper. Serve over the whipped parsnips.