Heat the oil and soy sauce in a wide skillet. Add the tempeh, stirring quickly to coat. Saute over medium-high heat, stirring gently and frequently, until golden and crisp, about 7 minutes.
Meanwhile, combine the mayonnaise, rice milk, and horseradish and lemon juice to taste in a small serving bowl and whisk until smooth. Stir in the dill.
When the fries are done, arrange them on a platter. Serve at once with the sauce.
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