Prep the carrots: Peel and slice the carrots into even pieces.
Aim for 1/2-inch thickness so they cook evenly and keep some bite.
Heat the pan: Place a large skillet over medium heat. Add the butter and olive oil. When the butter melts and foams, you’re ready.
Start the carrots: Add the carrots and a pinch of salt.
Toss to coat. Cook for 3 to 4 minutes, stirring occasionally, to get a bit of color.
Steam to soften: Pour in 1/4 cup water or stock. Cover the pan and let the carrots steam for 4 to 6 minutes, until just tender when pierced with a fork.
If the liquid evaporates quickly, add a splash more.
Add flavor: Uncover. Stir in the honey, thyme, and garlic (if using). Cook for 2 to 3 minutes, stirring often, until the liquid reduces and the carrots look glossy.
Finish with acid: Turn off the heat.
Add lemon juice (and zest, if using). Taste and adjust salt, pepper, and honey.
Serve: Transfer to a warm dish, spoon over the glaze, and sprinkle with a few fresh thyme leaves. Serve right away.