I remember my son just deciding one day that he was no longer going to eat purees. I had a freezer full of them and he didn't want to eat them. I started making him puree sandwiches with soft whole wheat bread or pitas. They also make great sauces for pasta for his little fingers to pick up and you can use 1/4 cup puree as a sub for an egg in your favorite waffle, pancake or muffin recipe. I would make those in quantity (and even do now after my frozen purees are long gone) and freeze them. It's really easy to pull a pumpkin muffin out of the freezer and pop it in the microwave or toaster oven for 30 seconds to thaw it. He also loved savory pancakes. Just take out the sugar, add some garlic powder or herbs and pureed spinach or broccoli. Other easy favorites are chopped fruit (banana, peaches, pear, berries, grapes, oranges), steamed or roasted veggies (peas, carrots, sweet potato, potato, corn), tofu, cereal, crackers, cheese. We're vegetarian, but little meatballs make good finger food at that age too.
A great site to check out if you want to make some of your own stuff is weelicious.com. She has recipes for everything from purees to older toddler food and you can search by dairy free or egg free or by age.