The truth is that I'm a bit slow when it comes to gardening fads. I'm totally clueless about most of that kind of stuff. [That's true for life in general, actually.] It's only lately that I've become aware of Deep Mulch Gardening. So, I read up on it and was pleased to discover that it's not a new thing at all.
Gardeners who hate weeding have been doing this forever. There are a couple of ways to do it. The first is to get your straw/hay/grass and fluff it up and spread it out in a 6 inch deep layer and let it sit. You can carve out your rows and hills inside it and plant. Works great.
Another way to deep mulch is to separate the bales into sections. What I generally do is use the bales that I've had around my cold frames all winter.
In the spring, I lift the bales out of the bed they were in and then dig/prep the bed. Then I separate the bales into sections. You can see in the pic the sections/thick layers that form as they're making the bales. The bale will fall apart or pull apart naturally at these places and leave you with a bunch of flat straw squares a few inches thick.
When I plant a row, I lay these out right next to the row to form paths. Here you can see the path next to the arugula.
Row planting: I plant all my rows one straw square apart. That is a good distance for growing most things. the straw paths are plenty wide for careful walking. The straw sections have already been pressed down so much in the baling process that they are an effective weed barrier. I don't fluff them at all. Works like a charm for weed control.
Hill planting: I plant the tomatoes and squash much further apart, but still separate the straw into squares and place them around instead of fluffing everything up.
Bed planting: When I plant greens in the cold frames or hoop house, I put a straw path down the center and then scatter the seed in two broad beds on either side, like this. [Since this is a winter bed, I've stuffed some extra straw around the edges where the cold might creep in.]
One caveat - If you get seedy straw [and there's no way to tell until it's too late], you'll get grass or wheat germinating around the edges of the squares. The good news is that these are easy to grab and weed and they'll come right out with little effort. I generally don't have to do that more than once a season.