Special equipment: 13 by 9-inch jellyroll pan
For the cake:
Pour 2 1/4 cups of the flour in a bowl with the salt, sugar and yeast. In another bowl, beat the eggs and add them, with the vanilla extract, lemon zest and cinnamon, to the lukewarm milk. Stir the liquid ingredients into the dry ingredients to make a medium-soft dough, being prepared to add more flour as necessary. I generally use about 2 1/3 cups in all, but advise you to start off with the smaller amount: just add more as needed. Work in the soft butter and knead by hand for about 10 minutes or half that time by machine. When the dough is ready it will appear smooth and springy: it suddenly seems to plump up into glossy life.
Cover with a kitchen towel and leave until doubled in size (1 hour to 1 hour 15 minutes). Or leave to rise slowly in a cold place overnight. Then punch down and press to line a jellyroll pan measuring 13 by 9-inches. You may think it's never going to stretch to fit, but it will, although you may need to let it rest for 10 minutes or so mid-stretch, especially if the dough has had a cold rise. When it's pressed out on the pan, leave it to rest for 15 to 20 minutes and then brush with the egg and cream mixture.
Meanwhile, preheat the oven to 400 degrees F.
Peel and chop the apple and toss it in a bowl with the blackberries and the zest from the other half lemon. Set the bowl aside for the few minutes it takes to make the crumble topping. Put the flour, ground almonds and cinnamon in a medium-sized bowl, stir to combine, then add the cold, diced butter. Using the tips of your fingers - index and middle stroking the fleshly pads of your clumpy (this is very buttery mixture) oatmeal. Fork in the sugars and sliced almonds.
Tumble the fruit over the egg-washed dough and then sprinkle the crumble on top of that. Put in the oven for 15 minutes, then turn down to 350 degrees F and cook for a further 20 minutes or so, until the dough is swelling and golden at its billowing edges and the crumble is set; don't expect it to be crunchy.
Remove from the oven and, if you can, wait 5 minutes or so before cutting it into greed-satisfying slabs.