Yes, I'd find out HOW MUCH egg-- and recall that it's done at
very high temperatures.
For example, in Yellow's brownie example above, we've
not tried-- even now-- anything that isn't WELL cooked, and it's only been in the past 10 months that this includes items made on the stovetop at all (pancakes, crepes, etc.-- she still doesn't eat undercooked egg in ANYTHING).
Everything else has ALWAYS been cooked to at least 325F, and often 350+. Plus, of course, being mixed with a lot of other ingredients.
DD started out with 1/96th of an egg baked like that into a batch of family sized brownies, spread SUPER thin (1/2") and baked for 30 min at 350F. We stepped her up and up for years, and then kept her at 1/20th of an egg daily for several years before trying an open egg challenge.
We truly NEVER expected that she'd outgrow. It was enough to be able to get her a flu shot, honestly. But having some commercial salad dressings, being able to have store-bought bread again, eating in a local diner when she wants a burger or sandwich... no specialty-made-in-Italy-pasta-- it's been LIFE changing just to not have to worry constantly about low-level cross-contamination. We did for many years-- no store-bread (cross contact with eggy varieties/washes), no commercial salad dressings (shared lines), only two brands of pasta, etc. etc. NO restaurants other than Taco Bell and
one local pizza place that we lost when they began making a gluten free eggy crust-- really not kidding.
The other thing is that egg, like milk, is just so darned hard for OTHERS to accommodate. KWIM? This is a big, big deal when they are in high school and college, and as they move into young adulthood. I'm so, so glad that we did egg when we did. It's been way, way better than I ever imagined.