Heat the milk until pleasantly warm to the touch (it's best to check its temperature with a thermometer, it should be 100-110°F (38-43°C)). The milk can't be too cold or too hot or the yeast won't work.
1/3 cup + 1 tablespoon (95g) milk
Add the milk to a small bowl, add the yeast, and 1/2 tablespoon of sugar. Stir together and set aside to proof for 10 minutes. After this time, the yeast should be foamy, if it's not, start over. It is not necessary to proof instant yeast, but I've found that when doing this, the dough rises better and faster and also, you can be sure that your yeast is working properly.
1 packet instant yeast
In the meantime, you can make the crumble: Add all the ingredients for the crumble to a medium bowl and work the butter into the dry ingredients with your fingers until the mixture resembles coarse crumbs. Place the bowl in the fridge.
3 tablespoons (42g) cold butter, 1/2 cup (62g) all-purpose flour, 3 tablespoons granulated sugar, big pinch of salt
To a medium/large mixing bowl, add the yeast mixture, flour, salt, and the remaining sugar (2 1/2 Tbsp). Stir together. Add the egg, egg yolk, and vanilla. Knead the dough by hand or with a stand mixer fitter with a paddle attachment until it comes together.
2 1/4 cups (280g) all-purpose flour, 1/4 teaspoon fine sea salt, 1 large egg, 1 large egg yolk, 2 teaspoons vanilla extract
Slowly add the soft butter, tablespoon after tablespoon, adding the next one when the previous one has been incorporated into the dough. Knead the dough for a couple more minutes until smooth.
5 tablespoons (72g) soft butter