In a large mixing bowl, add the eggs, yogurt, sugar, oil, and vanilla extract. Mix well with a whisk.
Grate the carrot and zucchini using the fine side of a grater. Add the carrot to the bowl. Squeeze the liquid out of the zucchini. There will be a lot. Squeeze as much as you can. Pull any large clumps apart before adding the zucchini to the bowl and mixing.
Add the flour, oats, coconut, cinnamon, baking powder, baking soda, and salt and mix. Stir only until just combined. Fold in the chopped dates.
Scoop the muffin batter into the liners. I use a 1 1/2 tablespoon cookie scoop and add two to three scoops to each liner, about 2/3 full.
Bake for about 22-24 minutes, or until a toothpick comes out mostly clean. Let cool for 5 minutes and then move the muffins to a cooling rack to let them cool.
Notes
Makes 12 larger muffins or 18 smaller snack-sized muffins.