Preheat the oven to 350 degrees Fahrenheit and line a 12-hole muffin tray with muffin liners.
Whisk together the full-fat canned coconut milk, eggs, and vanilla extract together in a large bowl.
Add the almond flour, unsweetened shredded coconut, sugar-free sweetener, baking soda, ground cinnamon, ground ginger, ground nutmeg, and sea salt (dry ingredients) to the mixing bowl and stir well until a thick dough forms.
Stir the grated carrot and chopped nuts into the batter until everything is well-combined.
Transfer the muffin batter to the prepared muffin pan, filling the muffin papers all the way up.
Bake on the center rack of the preheated oven for 30 to 35 minutes, or until the muffins test clean.
Allow the muffins to cool completely before glazing them and serving. If you're making the optional glaze, simply stir the sugar-free powdered sugar and lemon juice (or water) together in a mixing bowl until it's creamy.
Drizzle the glaze over the muffins.
Serve the muffins and enjoy!