Preheat oven to 350°F
Shred zucchini and sprinkle with roughly a teaspoon of salt, let this sit for at least 20 minutes to remove some of the vegetable's natural water. Drain the zucchini in a sieve or wring through a cheesecloth to remove excess liquid.
Combine both sugars, salt, and mix thoroughly with eggs.
*When a recipe calls for both brown and white sugars, mix those together first in a separate bowl to work the lumps out. Always add sugar to cracked eggs, and not the other way around, sugar can dehydrate eggs if not mixed together quickly.
Add tempered mascarpone and whisk until there are no lumps (or lumps are are smaller than a pea).
Add oils, and mix.
In a separate bowl, combine flour, baking soda, and baking powder.
Mix dry ingredients into the egg mixture.
Add drained zucchini and mix thoroughly.
Portion into lined muffin cups and bake for 19-23 minutes.
*When checking for doneness, don't just use the spring back test on these. Zucchini holds so much water that the top can be done and springy but not all the way down to the bottom. Use the toothpick test and make sure it comes out clean.
Allow muffins to cool before glazing.
Add all ingredients to a small pan and heat on medium-low (just enough too melt the butter) and combine.
Cool to room temperature.
Brush on cooled muffins and enjoy!