1. Stir the fresh yeast into the buttermilk in a large bowl, or the bowl of the standing mixer (it will be a real chore to knead it by hand). Sprinkle a spoonful of sugar and leave to foam up a little, about 30 minutes.
2. Add the remaining sugar, flour, salt and eggs to the bowl and mix with a dough hook attachment for 10 minutes at high speed until the dough gathers into a ball and, ideally, bounces off the walls of the bowl.
3. Turn the speed down to medium and add the butter by a tablespoon, waiting for each one to be absorbed. Scrape the sides of the bowl if necessary. The dough should be smooth, glossy and very sticky. Place it in a lightly oiled bowl in a warm place for 2 hours, till it doubles in volume; then chill it in the fridge overnight.
4. To make the crumble, place all the dry ingredients in a bowl and dice the cold butter into it. Rub the butter into the mix with your fingers (or pulse it in a mixer) until it turns into coarse breadcrumbs. Chill overnight.
5. The next day butter a 20 x 30cm cake tin with removable bottom or an ovenproof dish. Take the dough out of the fridge and gently transfer it to the dish (if you failed to oil the bowl, prise the dough gently off the bowl with a spatula). Try to handle the dough as gently as possible, stretch it roughly over the base of the dish.
6. Halve and stone the plums and arrange them over the brioche; push each half in. Sprinkle the raisins in between the plums, if using. Loosely cover with cling film and leave in a warm place for about 1 hour, until the dough plums up significantly and puffs up in between the plums.
7. Preheat the oven to 180C (no fan)/350F/gas 4.
8. Press the plum halves in if they rise up too much, sprinkle them with cinnamon and sprinkle the cake generously with the crumble topping (straight from fridge). Transfer to the oven and bake for 35-40 minutes, until the brioche has risen evenly, has coloured golden brown and the crumble is crisp.
9. Cool the brioche in the tin on a cake rack for 15 minutes, then remove the sides and let the cake cool down to room temperature. If it is baked in a ceramic dish, leave it in until cooled.