In a large mixing bowl, add sugar, coconut oil, and the zest of a lemon. Using a handheld blender, or in the bowl of a stand mixer, beat together for 1 minute or until light in color and fluffy looking. Add in eggs, one at a time, beating after each.
In a small mixing bowl, combine the milk, coconut extract, and the juice of the lemon. Mix together with a fork or a whisk.
In a separate small mixing bowl, combine the flour, baking powder, salt, and poppyseeds. Mix together with a fork or a whisk.
Alternate adding the dry ingredients and the wet ingredients into the sugar/egg mixture in the larger mixing bowl. Add half the dry ingredients, mix just until combined, then add half the wet ingredients, and mix just until combined. Repeat this one more time.
Divide the batter among the 12 cupcake liners. Fill each cupcake liner with batter. Each muffin cup will be almost full of batter.
Cook for 16-20 minutes or until toothpick inserted in middle comes out clean. The muffins will be tall and round with small cracks on the top.
Let the muffins cool in the pan for 3-5 minutes and then remove them to a cooling rack to cool completely. If you glaze them while they're still warm, the glaze will sort of melt into the muffin. Or, wait about 20 minutes and then glaze them and the glaze will stay on the muffins (like in the picture).
To make the glaze: Combine the glaze ingredients in a bowl and mix together. Either drizzle the glaze over the muffins, dunk the muffins in the glaze, or frost each muffin with the glaze. Add more or less powdered sugar/milk to attain the consistency of glaze you want.
You will need 1 lemon for the muffin batter. Be sure and zest it first and then cut it in half and juice it. You will add the zest into a different batter than the lemon juice.
You do not need to add the lemon zest to the glaze. Fresh lemon zest can be a bit strong so be careful of that if you are serving these to guests or to little children. My kids did not like the lemon zest in the glaze but I loved it!
The coconut oil comes in a jar and it's solid. You will need to melt it in the microwave and then add it into the batter, in it's liquid form. They also sell coconut oil already melted but it's very expensive compared to the solid form in the jar.