Socks without heel flaps

I would like to find a pattern that does not use a heel flap, but looks more like bought socks, with a “seam” to the heel.

What you want to look for is a pattern with a short row heel. There are tons of them to choose from, but here is a basic one. There is also a section on short row heels and toes here that you’ll want to check out – it’s got links to tutorials and such (scroll down). HTH