Preheat the oven to 375 degrees F. Line or grease a muffin pan and set aside (if using a silicone muffin tin, no need to line or grease).
Combine the flour, baking powder and soda, cinnamon, and salt in a bowl. In a small bowl, mix together the flaxseed meal and water, and let sit for 5-10 minutes to thicken (this will be your flax "eggs"). Prepare the other ingredients while you wait.
In a large mixing bowl, whisk together the flax eggs, mashed banana, maple syrup, olive oil, and vanilla extract. Stir in the grated carrots, followed by the dry ingredients. Next, stir in the raisins and mix until combined.
Scoop the batter into the prepared muffin tin. Each cup should be about ¾ full. Top each muffin with chopped pecans.
Bake for 20 to 22 minutes, until a toothpick inserted in a muffin in the center of the pan comes out clean. Let the muffins cool for about 5 minutes before eating. Transfer to a rack to cool completely before storing.
Olive oil: Using olive oil can impart a subtle fruity/peppery taste to baked goods. I personally love it! But if you want something more neutral, use the same amount of melted coconut oil or butter instead. Keep in mind that butter is not vegan, in case you need/want these to be vegan. If using coconut oil, measure ½ cup after you melt it.
Maple syrup: Substitute honey if needed/desired.
Flax eggs: You can substitute two regular eggs for the flax "eggs" instead (but they will no longer be vegan).
Pecans and golden raisins: Substitute chopped walnuts for pecans and regular raisins for golden ones if that's what you have on hand.
Storage and Freezing: Let the muffins cool completely, then store in an airtight container on the counter for up to 3 days (if they last that long!). To freeze, let the muffins cool, then store in a freezer-friendly bag or container for up to 3 months. For an extra layer of protection from freezer burn, wrap each individual muffin before freezing in a bag/container. Thaw in the fridge or on the counter overnight.
Reheating: If you want to reheat a muffin before eating, microwave for 15 seconds or place on a baking sheet under the broiler in the oven for a few minutes. They taste great with peanut butter!
Equipment: This is the silicone muffin pan I use and I LOVE it! It makes baking and clean-up so easy, and you don't need to spend any effort getting the muffins out.