"He's a sweet little owl, isn't he."

I just knew that I could turn the pom pom technique into something! I've created a pom pet pattern, dubbed the Pigwidgeon Pattern for it's obvious resemblance to a certain tiny grey owl, to follow:

The Pigwidgeon Pattern
One 4-finger-pom
One 2-finger-pom
Two knitted wings

• Using 4.0 mm needles and the long tail cast-on method, cast on 5 sts and leave a long tail for assembly purposes!
• Purl 1 row
• Knit 1 row
• Increase between the 1st and 2nd sts and 4th and 5th sts, using your favorite increase method. (I chose to pull the stitch up from below.) [7 sts]
  
• Knit 1 row
• Purl 1 row
• Knit 1 row
• Purl 1 row
• K2tog, K3, K2tog [5 sts]
  
• Purl 1 row
• Knit 1 row
• Purl 1 row
• K2tog, K1, K2tog [3 sts]
• Purl 1 row
• Cast off and weave in the end.

For a detailed pom pom production instructional video, see this post.
Begin 4-finger-pom by wrapping your chosen yarn around 4 fingers. Don't do this too tightly or you won't be able to extricate your fingers when you're done!
I wrapped the yarn around 75 times in order to get a very fluffy pom.
Cut the end of the yarn and then cut yourself a piece (sufficient in length) to tie around your yarn bundle. I like to use a self-cinching or surgeon's knot (which just means making your regular shoe tying over-under and then going over-under again). Tie it tightly because this is what holds your yarn critter together.
Snip the yarn through the loops where your fingers were. You have removed your fingers by now right? Good.
Time to fluff up your pom pom and give it a little trim so that it is round and even all the way around. Don't get overzealous with the hair cut though!
Make another pom pom via the same method using just 2 fingers this time. There, you've got the body the head and the wings!

Assembly

Using a yarn needle and some of the same yarn from the critter construction, sew on the head pom (smaller) by going up through the body pom (larger), back down through the head pom, and back through the body pom. You can do this as many times as you think are necessary to make it sturdy, but I've just made 2 passes and tied it off. [Make sure that you're going through the centers of the poms, otherwise the yarn will just pull through the sides!]

Threading the long tail from one of the wings onto the yarn needle, pass the needle through the body pom (at the desired wing possition) and use that end to secure the opposite wing. Do this by sewing through the 5 sts on the opposite wing and then back through the body pom and knot the yarn so it won't slip back through. Trim it to blend in with the body pom. Thread the tail from the opposite wing on the yarn needle and use it to sew on the first wing in the same fashion. Make sure that you pull the wings in close enough to the body, you don't want them to be too floppy!

Now you just have to find something for the eyes and beak. Little googley eyes from the craft store are easy to work with and you just have to hot glue them in place. Some felt glued on for the beak works quite nicely (just 2 little triangles, trimmed to fit).