Sorry if this sounds obvious, but why don’t you just take a smaller amount from the freezer? Or cut the single piece of broccoli, etc., in half (if you’ve got a good knife)?
Also, as much as I hate to waste food, you are basically throwing away what amounts to a single or half a hunk of broccoli every few days. It’s not a huge amount and not at all significant in the grand scheme of food waste.
contrary to popular belief, freezing them preserves the nutrients! The nutrients in fresh produce will eventually break down as they sit out, but freezing essentially puts a pause on that nutrient breakdown. This varies depending on how long you wait to freeze the produce, and of course how long you keep it frozen (but that won’t matter until you reach about a year).