Step 1: Heat the butter and oil in a large saucepan over medium heat. Add diced vegetables and saute until they begin to caramelize, about 5 minutes.
Step 2: Stir in honey and cook 1 minute. Add the vinegar and continue to cook, stirring, until it has evaprated, 3-4 minutes.
Step 3: Stir in the salt and pepper. Add the broth and whole thyme sprigs. Raise heat to high and bring to a simmer. Lower heat to medium-low, cover the pan, and simmer until the vegetables are tender, about 5-7 minutes.
Step 4: Drain in a colander and remove thyme sprigs.
Step 5: Transfer to a warmed serving dish and toss with thyme leaves from third sprig.
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