Make sure the carrot pieces are of even thickness so they cook evenly.
Melt the butter in a large deep skillet with a fitted lid or medium pot over medium heat. Add the carrots, olive oil, salt, pepper, and thyme and toss to coat.
Cover and cook over medium to medium-low heat for 18 to 20 minutes, stirring occasionally, until the carrots are tender when pierced with a fork.
Stir in the honey and cook uncovered for 2 to 3 minutes, tossing until the carrots are lightly glazed.
Remove from heat and stir in the parsley and lemon zest. Serve warm.