Preheat oven to 425°F. Line a baking tray with parchment paper.
Strain and squeeze zucchini from liquid and transfer zucchini to a plate lined with paper towel. Let zucchini sit for 5 minutes on paper towel to absorb more liquid.
In a large bowl, stir together avocado oil, dill, cilantro, salt and pepper. Gently toss zucchini into mixture coating well.
Divide zucchini mixture onto prepared baking tray and create 4 equal bundled portions. Create a small well in each bundle. Crack eggs into each well. Bake for 20 minutes or until eggs are cooked to desired doneness.
To serve: place 2 zucchini nests with a side of sliced avocado onto each plate. Garnish with dill sprigs, chili flakes, salt and pepper.