Mill millet, white rice, and gluten-free oats as finely as possible. Measure 70 g millet flour, 70 g white rice flour, and 40 g oat flour into a bowl. Add 110 g tapioca starch and 50 g potato starch. Whisk very well to evenly combine and break up any lumps. This is your 340 g flour blend.
Make the psyllium gel: In a small bowl, whisk 9 g psyllium husk powder into 105 g warm water until no dry spots remain. Let sit 3–5 minutes until thick, glossy, and stretchy.
Bloom the yeast: In the bowl of a stand mixer, combine the 300 g warm milk, 50 g granulated sugar, and 9 g active dry yeast. Stir and let sit 5–10 minutes, until foamy and expanded.
Add the psyllium gel, 2 large eggs, 56 g melted butter, and 5 g apple cider vinegar to the yeast mixture in the mixer bowl. Whisk or stir until the wet ingredients are well combined.
With the mixer fitted with the paddle or whisk attachment on low speed, add the flour blend to the wet ingredients a little at a time. Once all the flour is in, increase speed to medium and beat for 4–5 minutes. The batter should be smooth, glossy, and very soft, thicker than cake batter but looser and more spoonable than traditional bread dough. If it seems extremely loose and pours readily, beat in 1–3 tablespoons additional flour blend; if it is stiff and holds a firm dough ball, add warm milk a tablespoon at a time.
Let the batter rest in the bowl for 10–15 minutes to fully hydrate. It will thicken slightly but should remain soft and scoopable, holding a loose mound briefly before slowly settling.
First rise: Lightly oil the top of the batter and cover the bowl. Place in a warm spot (80–90°F) for about 30–45 minutes, until visibly puffed and slightly domed. It may not double but should look lighter and aerated. I used a temperature-controlled, proofing box.
Generously butter a deep-dish pie pan (9–10 inches, at least 2 inches deep). Scrape the risen batter into the pan and spread it into an even layer with a spatula, smoothing the top.
Arrange about 450 g (roughly one 16-ounce jar or can) drained, sliced cinnamon apples or apple pie filling evenly over the batter in a single layer, leaving a bit of space at the edges if desired to prevent overflow.
Make the cinnamon swirl: In a small bowl, mix 113 g very soft butter, 150 g packed brown sugar, 12 g ground cinnamon, and a pinch (about 1 g) fine sea salt until it forms a smooth paste. Dollop this mixture all over the apple-topped batter, then use a knife or spatula to gently swirl it through the top, creating marbled streaks without fully mixing it in.
Second rise: Cover the pan lightly and let the assembled cake rise in a warm spot for another 20–30 minutes. It should puff slightly and look a bit lighter.
Meanwhile, preheat the oven to 350°F (175°C). Place the pan on a baking sheet to catch any potential drips.
Bake on the center rack at 350°F for 35–45 minutes, until the top is deeply golden, the edges are set, and the center no longer looks wet. A toothpick or skewer inserted in the center should come out with moist crumbs but not raw batter.
While the cake bakes, make the cream cheese glaze: Beat 85 g softened cream cheese and 14 g softened butter together until very smooth. Add 120 g powdered sugar, 5 g vanilla, a pinch of fine sea salt, and 1–2 tablespoons of milk or cream. Beat until thick but pourable, adding a few drops more milk if needed to reach a drizzling consistency.
Cool the cake in the pan for 15–20 minutes. While still warm, drizzle the cream cheese glaze generously over the top, letting it run into the swirls and apple pockets. Serve warm in wedges, and store leftovers covered at room temperature overnight or in the fridge after that. Rewarm gently for best texture.