Preheat the oven to 375 degrees F and grease a standard muffin tin with nonstick spray.
Place all ingredients into a medium bowl and stir together gently to combine. Divide the batter among the prepared muffin tin, filling each about 3/4 full.
Bake for 18-20 minutes or until the edges are lightly golden brown and a cake tester inserted into the center comes out clean. Remove from oven, let cool in the pan for a minute or two, then transfer to a wire rack to cool at least slightly.
Serve warm or store.
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Notes
Use just the top parts of each broccoli floret and avoid using any of the harder stems. This will help ensure a fluffy overall texture to the muffins. You can chop the tops of the broccoli florets or cut that part off with a pair of kitchen shears.
Use a box grater to grate the carrot. You'll need about 1-2 medium or large carrots.
Use gluten-free cup-for-cup flour blend in place of the whole wheat flour to make these gluten-free.
To store, place cooled muffins into an airtight container and store in the fridge for up to 5 days. Reheat for 15-30 seconds and serve warm. Or freeze for up 3 months in the freezer in a zip-top storage bag with as much air removed as possible. Thaw in the fridge or at room temperature and warm to serve.
These pair nicely with soup and salad, or are a nice lunch or breakfast main dish with simple sides such as fruit, eggs, or additional veggies.