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Heat butter and olive oil in a large skillet over medium-low heat.
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Add brussels sprouts and apples; season with salt and pepper.
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Add rosemary and cook over medium heat, stirring occasionally, for 8 minutes, or until tender.
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Prepare walnuts by melting butter in saucepan.
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Add sugars and stir until incorporated; add walnuts and continue to stir around for about 2 minutes.
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Remove from heat and set aside.
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Remove brussels sprouts and apples from heat and let cool for 2 minutes.
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Spoon salad onto plate and garnish with candied walnuts.
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Serve.