I second this. Lots of 'self-sown' laurel in my garden and I spend ages cutting it back / down and it always sprouts again from the cut surfaces.
I put self-sown in quotes as many (most?) laurels grow out to the side and if the shoot touches the ground it roots itself. AFAIUI a single one with space around it will tend to grow vertically and be okay (apart from getting big - one of mine is c. 30' tall) but if they are close together they create shade and cause each other to root into the ground.
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