Add the butter to a large skillet over medium-high heat. Once foamy and melted, add the carrots and parsnips and cook, while stirring, for about 3 minutes. Pour in the chicken broth and 3 tablespoons of the honey and stir to combine. Turn the heat to medium, cover with a lid and cook for 5 to 6 minutes.
Remove the lid and season with the parsley, paprika and some salt and pepper. Turn the heat to medium-high and cook, while stirring, until the carrots and parsnips are tender and they're nice and glazed with the honey sauce, about 5 minutes more. Add the remaining honey and remove from the heat.
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