Decide your end goal: crunchy carrots (use parsnip grated) or soft moisture (use sweet potato, butternut squash, or pumpkin).
Swap at a 1:1 ratio for grated/mashed substitutes; if using bell pepper, start at ¾ of the carrot amount and cook until soft.
For baking, squeeze excess moisture from zucchini and drain/adjust very watery purées before mixing.
Taste and fine-tune: add a pinch of salt to bring out sweetness, and balance flavor with cinnamon/spice if your recipe uses them.
If your batter seems looser than expected, thicken with a tablespoon of flour or reduce mix-ins slightly.