Other than digging up a spot for more carrots this year, it will be no till. I'm picky about the carrots and like to get as many rocks out as I can, and sometimes add some sand for better drainage.
I have used both till and no till over the years, but have tilled twice in the last ten years. Last Fall I mulched with grass clippings and leaf mold, topped with about 2 feet of leaves and 'greens'. The downside of this method here is that it takes longer for the ground to warm up in Spring... here, where we can't afford to lose too many days.
If I don't get around to soil tending in Fall and the soil seems compacted, we may till in some compost, or just fork it up a bit, plant and then mulch.
Unfortunately, the 'weed' that will move in if I don't mulch is reed canary grass, and nothing will out compete it.