Preheat the oven to 350°F.
Line the bottom and sides of a 9-inch square baking pan with parchment paper (no need to grease the pan, since these blondies have plenty of butter!).
Stir the non-dairy milk and ground flaxseeds together in a small bowl or container. Let the mixture sit for at least 5 minutes, to gel.
Whisk the flour, cornstarch, baking powder, salt, and cinnamon together in a large mixing bowl.
Place the melted butter, brown sugar, and vanilla extract into a second large mixing bowl, then beat them together using an electric mixer at high speed for about 1 minute, until fully combined.
Add the flax mixture to the bowl containing the butter mixture. Beat the two mixtures together at high speed until creamy and slightly pale, about 2 minutes.
Begin stirring the flour mixture into the butter mixture, adding about a third at a time and stirring by hand just until combined. The mixture will be thick, like cookie dough.
Once the dry ingredients have been added, fold in the white chocolate chips.
Spread the batter into the prepared pan, smoothing it into an even layer.
Bake the blondies for 20 to 25 minutes, until the tops feel set, the edges begin to pull away from the sides of the pan, and a toothpick inserted into the center comes out clean.
Place the pan on a cooling rack and let the blondies cool completely.
Slice and serve.