I stumbled across a number of vector tutorials the other day, some of which are excellent for laFraise designers.
First of which is How to Illustrate a LeBron James Cartoon Character. Great style and technique in this one, def worth a try.
Another is one I had recently done for Computer Arts UK. Specific to tshirt designs and you might find some of the tips handy. Full tutorial is downloadable here.
And last but not least is not so much a tutorial as it is a general illustrator lesson. Checkout Improve Your Designs Skills by Luke O’Neil for some great tips.