Adult Harlequin Bug, a type of stink bug. They love brassicas, apparently.

I don't see a lot of big white bugs that fly. Could it possibly have been pale yellow with black striping? In that case it might be a cicada killer wasp. They don't seem to mind flying around humans or flying low to the ground when humans are around, but they won't hurt you. Since you said you were mowing tonight, it could be some sort of moth that comes out at night? Maybe something like the white lined sphinx? There's so many thousands of insects around and I doubt any of us have seen more than a small percentage of the ones found in our areas. You might try the website bugguide.net. You can click on a line drawing at the left that most resembles the shape of what you saw, and see where that takes you. It might take you to a page that has what you saw somewhere on it. On the linked webpage, there are images of insects commonly found in OK. Maybe you'll see a photo of it there. Insect Identification--Insects of Oklahoma

James, now that tsugajunkie has identified the eggs, you should look up squash bugs so that you can ID the adults and the nymphs. In the meantime, squish any eggs that you find.

I was out scouring all 6 blueberry bushes this morning and there is NOTHING on any of them. I did have some japanese beetle damage a bit ago, but that has tapered off. This is such an odd little "piece of overcooked oatmeal" (love that!) I also saw another bug on the blueberries a couple weeks ago. Wasn't able to get a pic, but another teeny beetle-ish thing I was not able to ID by going through all the insects in NH (all 895 of them!) So now I've found 2 rogue, single insects of some sort on my blueberry bushes. Oh well. Was just curious what this might be. Did more reading on scale and it sounds like when they are moving they are much, much tinier. I'll keep my eyes peeled for anything else out there. At least thus far it seems to be a single critter.