Tenacious, super-strong weeds like burdock will poke through your cardboard and mulch, which isn’t fatal to anything…but I like to at least set them back a bit by digging up the worst ones before laying down my materials, so the veggies can get started before competitors come on the scene. Here’s a post about this on the blog, with a link to an English garden blog that discussed it this spring, too: https://awaytogarden.com/cardboard-as-mulch#more-65 You can lay the cardboard and mulch first, then cut slits or X’s in it to poke your transplants or seed into, or plant your vegetables and then paper and lunch around. Depends on your planting plan–it’s easy to apply the cardboard and mulch after you plant if you’re working in rows, but in an irregular pattern you couldn’t. It will be easier if you can work in rows, frankly, because then all you’re leaving open (unpapered) is a relatively narrow strip of soil for a row of beans to be sown or a row of tomato plants to be planted in…and then you run cardboard parallel to it on both sides and so on. Don’t just plant in the mulch, however.