first time cover crop questions?? Advice please

I'm sowing a cover crop of buckwheat in some garden beds that Im leaving to fallow for the season. Also planning on planting a winter cover crop over the whole garden this fall.

What is the best way to sow these cover crop seeds?

Right now I have a 5" layer of hay mulch set down on the beds. My question is this:

Can I just broadcast these cover crop seeds directly into the mulch? Or do I need to pull back the mulch in order to plant the seeds?

I don't really want to leave the soil bare for weeks while I wait for the cover to grow in, and I don't really want to remove all of that mulch as it is in the process of decomposing and enriching my soil.

What's the best thing to do?

I would pull back the mulch and seed. Recover earth and seed with thin layer of mulch. Another way is to rake the seed into the soil a bit, then cover with hay. Or better cover with straw, hay tends to heat up if it is green. Laying down small sticks provides some edge that can help to hold seeds in soil and mulch from blowing away. Oats grow with buckwheat well here. Avoid thick hay mulch it will mat up and heat up. I have buried it under rows, which is way too much work, and seen good results.

I think Ryan has the best answer here - it's hard to beat a good 1/2" of soil to give the seeds a good footing.

If you REALLY don't want to pull off the extra mulch, consider broadcasting more seed (like one every square inch!) into the mulch and disturbing it to shake them down close to the soil. Then water really well and do a buckwheat dance over the whole area.
Oh, and think of planting a few peas or favas on the sunny edges -- abundance trumps fallow

For such a soft, tender plant, I find buckweat surprisingly capable of pushing through thick mulch, let alone thin.
I'd pull mulch back, rake seed in, sprinkle a light layer back on. I had a nice summer mix of buckwheat, crimson clover, borage and phacelia last year. The insects were overjoyed!