Preheat the oven to 375 degrees(F).
In a large mixing bowl or the bowl of a stand mixer, beat together the vegan butter, cane sugar and lemon zest with a hand mixer or the paddle attachment of the stand mixer, until the butter is light and fluffy.
Add the maple syrup, applesauce and vanilla to the bowl. Continue to beat until fully combined.
Now, in a separate medium sized mixing bowl, sift 1 3/4 cup flour, reserving the remaining 1/4 cup for later, the baking powder and baking soda. Stir in the salt.
Then, add the dry ingredients to the wet ingredients, alternating with the non-dairy milk, beating together the whole time until everything is fully incorporated.
Using the mixing bowl you had the dry ingredients in, toss the mixed berries with the remaining 1/4 cup of flour. Coat all the berries.
Then pour the berries and flour into the batter and fold into the batter.
Put muffin liners in a muffin pan. Using a large 6 muffin tin or small 12 muffin tin, fill the liners 3/4 of the way full.
Bake, if using a smaller muffin tin for 18 to 20 minutes or larger muffins for 25 to 30 minutes or until a toothpick comes out clean.
Let the muffins cool completely, then make the glaze.
Whisk together all the glaze ingredients, then generously pour on top of each muffin.
Let the glaze harden and then enjoy!