Using a vegetable peeler, peel ribbons from the zucchini, carrots, and yellow squash. Set the ribbons aside.
In a medium bowl, mix together the whole wheat flour, butter, coconut oil, and salt. Using 2 thin butter knives, or a pie butter, pull the knives past each other in the mixture so that the butter and oil are cut into smaller chunks and mixed in the flour until the chunks are about the size of peas.
Mix the ice water into the flour using a wooden spoon to combine and pack the mixture.
Once the crust has started to come together, pour into a 10 inch pie pan and press it down to form a solid layer along the bottom and the sides.
Line the walls of the pie crust with the veggie ribbons until the entire pie has been filled.
Season the pie with thyme, oregano, salt, pepper, a drizzle of olive oil, and parmesan cheese.
Bake for 30-35 minutes, until the crust has set and the cheese has melted.
Allow the pie to cool for at least 20 minutes before slicing.