Two stages, and the order is what makes these taste more like carrots than carrots usually do.
First a long gentle cook, covered, where the carrots soften in butter and honey without browning at all. Then high heat, uncovered, where the liquid reduces down to a thick sticky glaze and the edges catch and darken.
Doing it the other way round, or doing only the second half, gives you roasted carrots. Fine, but not this.

Worth saying plainly. The recipe as written calls for a steam oven set to 185F at full humidity for the first forty five minutes, which is not equipment most kitchens have.
The conventional oven version works and I have written it into the method below. Cover the pan tightly with foil and cook at 300F for forty five minutes. The foil traps the moisture coming off the carrots and creates a small steamy environment inside the pan, which is what the steam oven was providing.
Not identical. The steam oven gives slightly more even softening. Close enough that you would struggle to pick them apart on the plate.
Carrots are full of starch, and slow gentle heat gives enzymes in the carrot time to convert some of that starch into sugar before the heat gets high enough to shut them down.
That is the whole reason these taste intensely sweet without much sugar added. Roast a carrot hard from the start and you skip that window entirely. The honey is helping, but most of the sweetness is coming from the carrot itself.
Cover the pan with foil, but do not seal it down hard around the edges.
Sealed completely, condensation collects on the underside and drips back onto the carrots, and they sit in water instead of steam. A loose scrunch around the rim lets a little moisture escape while keeping most of it in.
Use a lightweight metal pan rather than glass or ceramic. It responds faster when you switch to high heat for the second stage.
It looks generous for a pound of carrots and it is not excessive. The butter is the body of the glaze, and there is only a single tablespoon of honey doing the sweetening.
Melt it before it goes on rather than dropping in cold cubes. Cold butter sits where you put it and the carrots underneath get coated while the ones on top stay dry.
Take the foil off, give the carrots a proper stir, and make sure every piece is coated in the butter and honey mixture sitting in the bottom of the pan.
Forty five minutes covered means the glaze has pooled underneath. Stirring redistributes it so the carrots on top get their share before they go under high heat.
430F with the fan on, uncovered, around fifteen minutes. Stir a couple of times so they brown evenly rather than only on one side.
You are watching for two things at once: the carrots browning properly, and the liquid reducing to something thick and sticky that clings rather than pools. When the pan looks nearly dry and the carrots have dark caught edges, they are done.
This stage moves fast at the end. Honey burns, and the difference between a glaze and a scorched pan is a couple of minutes. Stay near the oven.

Hot, with extra salt and pepper at the table.
They can be made entirely ahead and chilled up to twenty four hours. Reheat in a hot dry oven, around 450F for eight minutes, which brings the glaze back to sticky rather than leaving it claggy.
Minced garlic stirred into the butter before it goes on the carrots is the easiest change. Orange zest is the more interesting one, since the citrus cuts the honey. Finely sliced ginger scattered through the pan works too and gives a bit of heat underneath the sweetness.
Baby carrots need only a scrub. Regular carrots should be peeled and cut in half lengthways, then into two inch pieces, so the sizes stay consistent and everything cooks at the same rate.
Two stage honey glazed carrots, softened gently under foil then browned at high heat into a sticky glaze.
The original recipe uses a steam oven at 185F / 85C with 100% humidity for the first stage. The method here adapts it for a conventional oven: cover tightly with foil and cook at 300F / 150C for 45 minutes, then uncover and finish at 430F / 220C convection for about 15 minutes. Nutrition per serving from source: 131 calories, 14g carbohydrates, 1g protein, 9g fat, 5g saturated fat, 23mg cholesterol, 309mg sodium, 276mg potassium, 3g fiber, 10g sugar. Can be made up to 24 hours ahead and reheated at 450F for about 8 minutes.