Preheat the oven to 350℉ (180℃). Set out a 9x9-inch (23x23cm) square baking pan (no need to line it) or a 10-inch (25-cm) round springform pan lined with one large square of parchment paper that sticks up the sides all around the pan, to prevent leakage of the filling through the seam between the sides and base of the springform pan. (Tip: crumple the paper, then smooth it out, and it will be easier to fit it into the pan.)
Add the melted butter, honey, and lemon juice to the baking pan you are using. Stir the tapioca starch (or corn starch) together with the 1 tablespoon of water to make a slurry, and add it to the pan. Stir together the ingredients in the pan to combine them somewhat and make a syrup.
Sprinkle the saskatoon berries in an even layer over the syrup. Set the pan aside.
In the bowl of a stand mixer or hand mixer, whip the butter and honey together until smooth. Add the eggs one at a time, beating well after each addition.
Add about a third of the flour and beat just to combine it.
Add the milk and vanilla, beat to combine.
Add another third of the flour, beat to combine.
Add the sour cream, beat to combine.
Add the remaining third of the flour, along with the baking powder and baking soda, and beat to combine everything until there are no pockets of flour remaining. Scrape the bowl with a spatula to make sure to incorporate any flour at the bottom of the bowl.
Drop the batter in spoonfuls evenly over the saskatoon berries in the baking pan, and then with a spatula carefully spread the batter to the edges of the pan, trying not to disturb the berries too much. Smooth out the batter on the top of the cake, making sure the batter touches the edge of the pan all the way around, to seal it and prevent the berry mixture from bubbling up too much.Note: if you are using regular flour, the batter will be looser and can be scraped from the bowl onto the berries, and will need very little evening out.
Bake for 33-38 minutes, until a toothpick inserted in the center of the cake (just into the batter, not into the berries below) comes out clean or with a few crumbs adhered to it. It is natural for the cake to have large cracks in the top, as the berries below expand while they are cooking and push the batter up somewhat. It will deflate again as it cools.
Let the cake cool in the pan for 10 to 15 minutes, then it's time to make the 'upside-down' part happen. Choose a platter or serving tray big enough to hold the whole cake, with space around it to catch any stray oozing of juices.
Invert the platter over the top of the pan. Put one hand (with a pot holder or towel over it) underneath the hot pan and one hand on top of the inverted platter, and in one smooth, confident move, flip the pan and plate so the plate is on the bottom and the cake slips down out of the pan and onto the plate.
Carefully remove the baking pan, and scrape out any stray berries that have stuck to the pan, and place them back into the empty spots on top of the cake. Tuck in any stray berries that slip over the sides of the cake, too.
Cut the cake into 9 squares (or wedges if you used a round pan) and serve warm with ice cream or whipped cream.
Keep leftover cake, covered, in the fridge for up to 3 days. Re-warm the cake before serving.
Notes
You can use fresh or frozen saskatoon berries for this recipe. If using frozen berries, use 3 heaped cups as they don't pack as closely together as fresh ones do, and use them directly from frozen (no need to thaw them first).If you substitute blueberries or other juicy berries, you'll need to increase the amount of tapioca starch or corn starch, as they produce much more liquid than saskatoons do.