Heat the oven to 170 C / 340 F with a rack in the middle. Grease a 23 cm / 9-inch springform tin and line the base with parchment. Halve 8 feijoas, scoop out the flesh with a spoon and chop it into 1 cm pieces. Peel the 2 topping feijoas and slice them 5 mm thick.
Beat the butter and sugar in a 4-quart / 3.8 L bowl with a hand mixer for 3 minutes, until pale and fluffy. Add the eggs one at a time, beating 30 seconds after each. Beat in the vanilla, lemon zest and milk. The mixture may look slightly curdled, and that's fine.
Add the almond meal, flour, baking powder and salt. Fold with a spatula until no dry streaks remain, then fold in the chopped feijoa gently so the batter stays light.
Scrape the batter into the tin and smooth the top. Arrange the feijoa slices over the surface, scatter on the flaked almonds and sprinkle with the demerara sugar.
Bake for 55 minutes. At the 35 minute mark, check the top, and if the almonds are darker than golden, tent the tin loosely with foil. The cake is done when a skewer comes out with a few moist crumbs and the center reads 96 C / 205 F.
Cool the cake in the tin on a wire rack for 30 minutes. Run a thin knife around the edge, release the springform and slice.