Hi Evan.
I have two kiddos, one is 3 and the other is 4, and they are vegetarian, though are egg- and dairy-free most of time. I've experienced similar phases with both of them, and to different extremes depending on personality. Usually for us, the pickiness is reflective of how many "treats" we've been having. The girls were sick a couple weeks back, so we had a lot of crackers, applesauce, Popsicles, etc, and next thing you know, they are feeling better but turning their nose up at reasonable healthy dinners, like burrito bowls, or pasta. Sometimes a gentle but firm option is what I've done, such as offering a banana when they want larabars. The banana is totally reasonable, and tasty, and eventually they will eat it. I guess the biggest thing is to know that you are providing them with a reasonable option, and they have a right to refuse, but that option will still be available when they get hungry.
Also, PB&J is a totally reasonable thing to have every day. I remember picking a sandwich at the beginning of the school year and my mom made me that same lunch every day for the whole year. Maybe give her some veggies to munch on while you put the sandwich together, then fruit when she's finished, and you have a meal.