Step 1Line 2 or 3 baking sheets with parchment paper then spray with nonstick spray. Dust lightly with bread flour.
Step 2Crumble the fresh yeast into the bowl of an electric mixer, or sprinkle in the dry yeast. In a small saucepan, warm the milk until it is no longer chilled and is just barely lukewarm, about 105 degrees. Pour the milk over the yeast and whisk to dissolve.
Step 3Add 1 1/2 cups of the pastry flour to the milk and whisk 2 or 3 times to just barely incorporate. Sprinkle the rest of the pastry flour over the mixture to cover the top. Do not mix this any further.
Step 4Cover the bowl with plastic wrap so that it is airtight, and place in a slightly warm place until the top layer of flour has cracked noticeably, about 4 minutes.
Step 5Meanwhile, remove the vanilla bean seeds by scraping the length of the bean with the back of a knife. Place the seeds in a saucepan with the butter and melt together over low heat. Set aside.
Step 6In a large bowl, whisk together the eggs, sugar and salt. Add the butter and quickly whisk it into the eggs. Pour the egg-butter mixture into the mixing bowl with the flour. Mix on low speed for a few seconds to incorporate the flour, then increase the speed to medium and mix 1 minute. Add the 3/4 cup of bread flour and mix on low for a few seconds, then on medium for 2 minutes. The batter will be lumpy and quite sticky. Transfer to a large greased bowl and cover completely with plastic wrap so it is airtight. Return the bowl to the warm spot and let rise until it doubles in size, 2 hours.
Step 7Once it has risen, sprinkle 1/4 cup of bread flour over the surface. With your hands, gently tuck the sides of the dough under itself to deflate it. Cover the bowl again and let the dough rise until it has doubled in size again, 45 minutes.
Step 8You will need a significant amount of bread flour to coat your work surface. Choose a surface that is cool to the touch. Sprinkle a thin blanket of flour over it, and using a pastry scraper, pour a third of the dough over the flour. Then sprinkle the surface of the batter with more bread flour. With the palm of your hand, gently press the dough down to about 1/2 inch thick. Dip the end of a 1 1/2-inch round cutter in flour and begin to cut the doughnuts out. Rather than picking them up with your fingers, use the cutter to push the doughnut off the end of the counter and on to the palm of your hand. Or try using a small spatula dipped in flour to lift the doughnut off the counter, careful to keep the round shape. Then gently place the doughnuts on the floured baking sheet. Repeat until you have cut all the doughnuts. Wrap the baking sheets with plastic and refrigerate the doughnuts as you work. (Bring to room temperature before frying.)
Step 9To fry, add enough oil to come halfway up the sides of a large saucepan and heat to 350 degrees. Drop the doughnuts into the oil, about 6 at a time, making sure you do not overfill the pot. Fry the doughnuts until they are golden on both sides, 3 minutes total. Drain on paper towels, then toss into a bowl of sugar to coat.