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Pour 1 cup (240 ml) of milk into the mixing bowl of a stand mixer. Add ½ cup (100 g) plus 2 tablespoons of sugar, ½ cup (95 g) of room temperature shortening, and 3/4 teaspoon of salt. Turn the mixer on to medium-low speed and beat the mixture for a minute or two, so the ingredients are combined. You'll want to use a stand mixer for this dough because it is really sticky to work with. Open 1 envelope (2 1/4 teaspoons of 7 g) of instant yeast and pour it into a small prep bowl. Pour in ¼ cup (60 ml) of warm water and 1 teaspoon of sugar. Stir the mixture, so the yeast and sugar dissolve. You should notice the yeast bubble a little as it activates. Pour the yeast mixture into the mixing bowl. Measure out 3½ cups (437 g) of flour and add half of it to the mixing bowl. Turn the mixer on to medium speed and beat the dough for 3 to 5 minutes. The dough will be very thick and paste-like once it's combined. Crack 3 egg yolks into the mixing bowl and add the rest of the flour. Turn the mixer on to medium speed and beat the dough for 3 minutes. The dough will be sticky at this point. You can discard or save the egg whites for another recipe.
Combine the milk, shortening, sugar, and salt. Activate the yeast. Stir the yeast and half of the flour into the mixing bowl. Stir in the egg yolks and the rest of the flour.