You can find some flat patterns for making mittens, hats, and "slippers" here:
just put in "flat" in the pattern search box.
You could also do a Google search for "two needle mittens"
Kate Gilbert also has a pattern for flat mittens here:
Also, if you want to knit in the round you could use two circular needles of the same size; similar to knitting socks on two circular needles.
The problem with knitting a flat hat or mittens is I don't think it will provide you with the new challenges you are looking for; due to the fact that knitting a flat hat is similar to knitting scarves, dish cloths, etc. with the extra added step of seaming your project close.
What you might want to try when reading your patterns is to ask yourself where does your yarn need to be for your next stitch. Like in the example you give. If you know how to purl and purl 2 together, you know that the yarn needs to be in the front for that to happen; so when you wrap the yarn over the needle you know you need to bring it forward under the needle to complete a purl or purl 2 together. Also, if you are knitting western style you also know you wrap your yarn counter clockwise to make new stitches. Just relax, trust yourself and you will soon get the hang of it.