Mix the puree with the egg and sugar. In a bowl, the 300 g of puree, the 50 g of egg, the 75 g of sugar and the 5 g of vanilla, whisked until smooth. With fresh yeast: crumble the 16 g over the mixture here and whisk until there are no lumps. With active dry yeast: dissolve the 7 g in 30 g of the reserve milk, warm, wait 10 minutes and add it here.
Add the flour. With the 5 g of instant yeast, the 7 g of salt, the 2 g of cinnamon and the pinch of turmeric. Mix with a spatula and then with your hands, or with the dough hook of a stand mixer on low speed, until there's no dry flour left. If there's flour that won't come together or the dough feels stiff, add milk from the reserve 10 g at a time, up to 60 g at most.
Let it rest for 20 minutes. Covered.
Work in the butter in three additions. The 70 g, without adding the next one until the previous one has disappeared. With a stand mixer: dough hook on low speed, about 3 minutes per addition and 3 more minutes at the end. By hand: about 15 minutes in total, pushing with the heel of your hand, folding and turning.
Knead until smooth and elastic. It's ready when it pulls away from the counter almost by itself. If it gets very soft or greasy, chill it for 10 minutes and carry on.