Pour the milk over the yeast in the bowl of an electric mixer fitted with the dough hook attachment. Let the mixture sit for 2 minutes to allow the yeast to dissolve, then whisk to combine.
In a large bowl, combine the flour, sugar and salt.
In a separate bowl, whisk together the eggs, orange blossom water, and orange oil.
Mixing on low speed, add the flour mixture and egg mixture to the yeast and milk mixture. Continue mixing on low speed for 3 to 4 minutes, until the dough comes together and begins to develop; it should hold together in a soft mass.
Increase the mixer speed to medium and add the butter a few pieces at a time until it is fully incorporated, then continue beating the dough for about 5 minutes, until it is soft and cohesive. Listen for the sound of the dough slapping the sides of the bowl; this is a telltale sign of a well-developed brioche dough. Pull on the dough to stretch it 3 inches across; it should stay elastic and not break. Form the dough into a smooth round and place into a large buttered bowl. Cover the top of the bowl with plastic wrap and refrigerate for at least 6 hours or overnight.
Line a 12-by 17-inch baking sheet with parchment paper or a silicone mat.
Liberally flour a work area and roll out the dough into a level, 12-inch square that’s just under a ½-inch thick. Brush off the excess flour from both sides of the dough. Using a 3-inch round biscuit cutter, cut out 10 to 12 donut shapes. Dip the cutter in flour and shake it off before each cut to prevent sticking. Place each donut on the prepared baking sheet, allowing 1 to 2 inches between them. Cover the donuts with a light dish towel and put in a warm place to rise for about 1 hour, until nearly doubled in size and soft and pillowy.
While the donuts are rising, pour the 2 cups sugar for rolling into a shallow bowl wide enough that you can easily handle the hot donuts in.
Pour safflower oil to a depth of about 3 inches into a large, heavy saucepan and heat over medium heat until the oil reaches 365°. It is important to keep the oil between 355° and 375°; if it is not hot enough the donuts will absorb too much oil, and if the oil is too hot the donuts will brown too quickly before cooking through to the center.
Using your hands, gently remove the donuts from the baking sheet and carefully place them, in batches of 3 or 4 at a time, into the hot oil. Fry for 2 minutes on each side (use a timer to help keep track of time so you do not undercook or overcook the donuts). Remove the donuts from the oil with a slotted spoon and place them on a paper towel–lined baking sheet to drain the excess oil for 15 seconds, then immediately roll in sugar. Put the donuts on a metal rack to cool completely, about 1 hour.
When the donuts are completely cooled, pierce through the side with a chopstick (or other dowel-like implement) to make a hole for the filling. Wiggle the chopstick around to enlarge the hole so the donuts can receive a generous amount of filling.
Spoon the jam into a pastry bag fitted with a ¼-inch round tip. Insert the tip into the donut’s hole and squeeze about 2 tablespoons of jam into each donut. Serve immediately; the donuts are best eaten the same day they are prepared.