Kelly, as with most things, it depends upon a few factors. First how coarse is your mulch, and second how hot and humid is your weather, for how long each year? Those two factors amongst others will determine how fast your mulch breaks down to compost.
Down here, a few hundred miles south of you, my Florimulch wood chip mulch dependably breaks down after about a year. But if I use large pine bark nuggets, it takes two years.
So, the answer is, if the mulch is still pretty recognizable as wood chips when you are ready to add more compost, just rake it or scrape it back from around your plants, add your compost and then re-distribute it over the compost again.
Btw, using just compost might not be quite enough to feed your vegetables until you get your soil richness built up. Might take a few years, so find an organic fertilizer you're comfortable with, and use that in the meantime. Nothing is more disappointing than to put in the work to grow vegetables and get a meager harvest.
