Step 1

Whisk whole wheat flour, salt, and 1 cup all-purpose flour in a large bowl to combine. Add butter and work into dry ingredients with your fingers, smashing between your palms to flatten, until largest pieces are the size of a nickel. Drizzle in 6 Tbsp. ice water and rake in with your fingers. Gently squeeze handfuls of mixture together until a shaggy dough forms. Turn out onto a work surface and knead until only a few dry spots remain. Pat into a disk and wrap in plastic. Chill until very firm, at least 2 hours or up to 3 days.

Step 2

Roll out dough on a lightly floured surface to about ⅛" thick. Transfer to tart pan. Lift up edges and allow dough to slump down into pan. Gently press into corners and trim excess. (If using springform pan, trim dough to 1½" up sides of pan). Freeze until firm, 15–20 minutes, or cover and chill up to 12 hours.

Step 3

Place a rack in lower third of oven; preheat to 350°. Swirl 2 Tbsp. oil in a large skillet to coat bottom and add yellow onions; season with kosher salt. Set skillet over medium heat and cook onions, stirring occasionally and making sure to scrape bottom of pan, until very soft and deep golden brown, 15–20 minutes. Add garlic and cook, stirring occasionally, until onions are caramelized and deeply browned, 25–30 minutes (if any pieces get super dark and stick to the pan, a few drops of water should dislodge them). Let cool.

Step 4

Brush mustard over chilled dough, then sprinkle with cayenne. Stir cheese into caramelized onion mixture and spread across crust in an even layer.

Step 5

Using a mandoline or very sharp knife, thinly slice both squashes crosswise. Cut sweet potato and red onion in half lengthwise, then thinly slice crosswise with mandoline. Arrange vegetables in concentric circles, with rounded edges facing up, starting from the outside edge, leaning slices against the crust, and working your way inward. Drizzle remaining 2 Tbsp. oil over vegetables and season with kosher salt.

Step 6

Bake tart until edges of vegetables are browned (a few spots may even get deeply browned) and crust is golden brown, 75–90 minutes.

Step 7

Melt thyme and butter in a small saucepan and cook just until butter is bubbling. Brush over tart with a pastry brush and sprinkle with sea salt.