You mention that today is a special day and thus, just one example. I totally get that. Those days happen. :)
On a typical day, you might start thinking about the amount of snacking she does. Is she grazing throughout the day, and thus, never getting full? Also, as you know, the type of foods that she eats will make a difference with how quickly she starts to feel hungry again.
Perhaps try to be a little more strict with timing. Have a good breakfast and then know that the morning snack will be at XX time. Afternoon snack will be at XX time. In between, pay attention to her requests for more food. Obviously, you don't want her to be hungry, so you may need to adjust what/when you're giving snacks. At snack time, have two or three healthy options set out. Let her choose which one she wants (or heck, she may want a little of each, and that's okay, too).
She's a growing girl, so there are going to be times that she needs to eat a little more.
On the Veggies, I used to struggle with this, because I personally don't like very many veggies. I commented on this to my mom several years ago, and she had a really simple answer that I now use quite a bit. Buy some small bags of frozen veggies (mixed veggies, peas, green beans, corn, etc.). Before each meal, have your daughter pick which one she wants. Pour a single serving into a bowl, **put water over the veggies (enough to cover the pile), and pop it into the microwave for a minute - 90 sec. Once it's done, drain the hot water off of it, and it will cool down enough to eat in another minute or two. It is SO easy to do. I always have the veggie sitting out when I tell my kiddos to get into their chairs. It is the only food on the table as I'm filling their plates, and they almost always have polished off the veggies by the time their plates arrive at the table. (and something unrelated, but fits...forget those expensive chip clips....just buy a pack of wooden clothesline pins for about $2 at the store and use those to close up each of the various packages of open frozen veggies before putting them back in the freezer to help keep the veggies fresh).