Make the dough:
In the bowl of an electric mixer with the paddle attachment, beat the butter with the sugar until combined, add the buttermilk. Beat to incorporate the buttermilk, scraping down the sides of the bowl.
In a separate bowl whisk together the flours and salt. Add the dry ingredients into the mixer with the butter and buttermilk in two additions. Mix until combined into a soft dough. Remove from the mixer, flatten into a disk, and refrigerate for at least one hour before rolling out
Whisk together the custard ingredients until well combined.
Slice the squash. In a dry saute pan, char the corn until nicely browned. Cool.
Assemble your tart:
Roll out the dough and form into a tart shell prepped with nonstick cooking spray. There will be leftover dough. Pour the custard into the tart shell.
Artfully arrange your vegetables on top of the custard by placing rows of squash, followed by rows of cherry tomatoes. Fill the gaps between the vegetables with the charred corn. Spray the entire top of the shell with more cooking spray, sprinkle with salt, pepper, and a handful of parmigiano.
Bake tart in a preheating 350 F oven for 30-40 mins until the tart shell is brown and the squash is cooked through.