Microwave your milk for about 30-40 seconds and then pour the milk into the bowl of your stand mixer and add your yeast into the milk. Let it sit for 10 minutes until foamy.
Next add in the sugar, softened butter, zest, eggs, salt, vanilla, and brandy. Mix with the paddle attachment until combined. Switch to the dough hook and add in 2.5 cups of the flour while mixing on low. Continue adding flour up to 3 cups, until it begins to pull away from the sides of the bowl and climb up the dough hook. If it appears that parts are not mixing in, or it's not picking up some of the flour, turn off the mixer and use your hands to mix it together a bit, then remove your hands, and turn it back on to let it knead some more.
Remove dough from the bowl and prepare a large bowl that you have lightly oiled with vegetable oil. Roll your dough in the oiled bowl a bit before covering with plastic wrap, and then a towel. Keep in a warm area of your kitchen for two hours for the dough to rise - until it doubles in size.
Once doubled, remove the dough, roll it into a long cylinder, about 2 inches in diameter, and cut into 24 parts, about 3/4 inch thick each. Roll each piece into a ball, and place onto a lightly oiled baking pan to rise again. Cover with plastic wrap and a towel and let rise 1 hour.
Fill your heavy saucepan about 3 inches deep with the vegetable oil. Heat on medium until 350F. If you don't have a thermometer, you can check by putting a wooden spoon in and see if the oil bubbles a bit - then it's ready. You can also throw in a small piece of dough to see if it is ready. Once ready, fry a few doughnuts at a time, about 40 seconds per side. Remove and place onto paper towels to drain and cool.
Use a knife to make a small hole in the side of the doughnut. Using a piping bag and round tip, fill bag with jelly, then pipe into the doughnut until jelly pokes out of the hole a bit. Dust with powdered sugar. Enjoy!