As much as this thing is a monster, it tastefully and effectively masks an ugly Costco vinyl shed and firewood shelter (think 3-sided box). But, it sure needs hedging...

You don't have to do all sides in one year, if its a serious reduction.

It can get hot in late May. Don't expose too much bare stem to the sun, like major cut-backs in late May to August. The bark can get sunburned.

I recall one guy - about 1989 - saying that English laurel was near indestructable, and defoliating it in June. It got "creamed" by the sun, with little foliage coming back that year, and bark peeling and cracking the next year due to the severity of sunburn.

So part of the timing answer, deals with how much you plan to prune or reduce.

The sides are safer from sun exposure than the top, especially if they don't face the sunset. Even if one side does face the sunset, it sounds very do-able now.

My laurel hedge has flowered in mid-spring every year since it was planted about 8 years ago. Lovely fragrant, white, droopy flowers. Most years we just gave it a light-ish trim whenever it got out of shape to encourage it to grow to the right height/width (approx 12 ft high). Last year it had got so big we gave it quite a heavy pruning in October. This year - no flowers! So when is the best time to trim so we still get flowers each year?