Position a rack in the center of the oven and preheat to 350°F convection or 375°F standard.

Peel the squash and use a mandolin to slice the pieces as thinly as possible. Add these slices to a large bowl.

Place a small pan over medium heat, add the 3 tablespoons of butter and let the butter brown. Stirring occasionally while the butter foams until brown flakes form at the bottom of the pan, around 3-4 minutes.

Add the brown butter to the squash, then squeeze in the juice from half a lemon. Add in 50 grams of brown sugar, 130 grams of granulated sugar, and mix until the squash is well coated. Set this aside.

In another bowl, whisk together three eggs and ½ cup of milk. Add the 140 grams of flour, 1 teaspoon of salt, and ½ teaspoon of ground ginger, nutmeg, and cinnamon.

Pour this over the butternut squash. Mix gently to combine.

Line a tart pan with two pieces of parchment paper, making sure the paper comes all the way up the edges.

Scoop the squash out of the bowl, shaking off any excess custard, and layer it into the pan. It doesn't need to be perfect, but you want the squash pieces to be able to bake into nice layers. When all the squash is in the tart, pour any remaining custard batter over the top.

Move the pan to a baking sheet to avoid any spilling. Give the sheet a few taps to let the batter settle.

Bake at 350°F convection for 60-70 minutes, or until the edges are pulling away from the sides and the center is firm.

When the cake is out of the oven, put it on a cooling rack.

Now make the ginger simple syrup. Add ½ teaspoon ginger, 75 grams sugar, and 2 teaspoons water to a small pot. Place this over medium heat, stirring until the sugar melts into a syrup. Pour directly over the cake. This will firm up into a sugar crust of sorts.

Dust with powdered sugar if you like, then slice and serve!