Black bean tacos (can just eat the black beans plain). Take can of beans, heat in pan with seasonings (we use garlic powder, onion powder, cumin and a touch of chili powder).

When my son was little, he loved cut up veggie burgers (now he won't eat them).

I found with most veggies, the key is trying different shapes and level of cooking (raw, steamed, stir-fry). My son now eats a ton (yes, it could be a lot of luck, but I like to take some of the credit). Try some of the stir-fry mixes from Trader Joes frozen section. Just separate them on the plate if your kid doesn't like things mixed.

I always offer several types of veggies and/or fruit. If there is variety, my son will choose at least one. But I mean EASY choices. Like defrosted frozen fruit. Trader Joes often has pre-cut fruit that is decent (at least sometimes).

One of our favorite super-quick meals -

Prepare any small pasta (acini di pepe, orzo, ditalini) and drain over frozen peas to thaw them. Rinse or let cool to almost room temperature and stir in cottage cheese (and parm, if they can/will eat it). I add loads of black pepper to my bowl. Fast, creamy and comfort-foody.

My DS loves roasted squash. We've recently discovered delicata squash which you can roast with the skin on. Cut them in half length wise, empty out the seeds, and then cut into 1/2 round pieces. Roast on a baking sheet with some olive oil for about 30 minutes (approx. 375 oven) turning occassionally.

This is a great one to practice using a spoon with.

http://www.marthastewart.com/275724/parsnip-recipes/@center/276955/seasonal-produce-recipe-guide#/257177

We also make a veggie-loaded turkey meatloaf.

While these aren't as fast as nuking the frozen veggies and serving with hummus or beans (which we do alot), they are easy to make ahead and keep well for busy weeknights.

At that age, my son would eat anything out of a pasta salad for some reason-- but that mean it had a viniagrette dressing on it. I figured that wasn't a huge deal- so I'd make some of the tri-colored "wacky mac" pasta for the veggies factor, then add black olives, black beans, carrots (but cooked and cup up very small), peas, etc.

He is 2.5 and still his favorite veggies are Edamame (the ones from Trader Joe's frozen section, cooked according to package directions. He shells them himself and thinks it's hilarious) and lima beans.

If she won't eat broccoli, try giving her just the stems, not the flowery part. My DS hates the tops but will gladly eat the bottoms.

Also, when it doubt, try feeding it to her off your plate. That's always more appealing, ha ha.

frozen mixed veggies were an early finger food favorite of all my kids.

Ohhhh... never thought of limas. Will have to give that a try.
1 year old DD loves avocado... which led to her swiping some california rolls from DH. They are a special treat for her
beans of any kind - they can be kind of bland, but you can season them up in various ways and they are a fun "finger" food. I give DD canned beans (GASP) which I rinse, rinse, rinse first.
I have found that DD will eat pretty much anything if she sees me eating it first. Then she MUST have some, lol! So sometimes I will purposely let her see that she is getting O's and mom is eating... something else. Then I let her "steal" some and down the hatch it goes.
Do you eat indian food? Saag paneer might be a good start.

My two year old loves this http://ronzonigardendelight.newworldpasta.com/pasta_story.cfm. She will also dip pretzel thins into guacamole (she really just uses the pretzel as a spoon). In addition, she really wants to eat things that she sees me eating...a little reverse psychology never hurt anyone.

My children ate frozen peitite peas but I think we started that at a little older than one. I mean they ate them frozen.