Cut off the ends off of the carrots (you do not need to peel them). Cut the carrots and potatoes into large, equally sized chunks.
Place the potatoes and carrots in a large stock pot. Cover with water and generously add salt. Bring to boiling and boil 5 minutes or until barely starting to soften and still very firm. Using a colander, drain the vegetables and let stand in the colander to dry slightly.
In the same stock pot, melt the butter. Stir in the honey, oil, thyme and vinegar. Return the carrots and potatoes to the pot; stir until they are well coated in the liquid mixture.
Line a baking sheet with foil. Arrange carrots and potatoes on the baking sheet. Pour any remaining liquid from the pot over the vegetables.
Bake 30 to 40 minutes or until caramelized and tender.