Dough: In a large mixing bowl of a stand mixer dissolve both packets of yeast in warm water with 1 Tbsp sugar. Let stand for 5-8 minutes until frothy.
To the bowl, add warm milk, vanilla, 1/2 cup sugar and eggs. Add the dough hook attachment, turn the mixer on low and stir together, then add 5 1/2 cups flour and salt. Mix on low, scraping the sides of the bowl as needed.
With mixer running, drop cubes of butter into the dough mixing well between each addition to incorporate.
Increase the mixer speed and knead the dough for 5-7 minutes adding additional 1/2 cup flour as needed, if too sticky.
Turn the dough out onto a lightly floured work surface and turn to coat with flour. Knead by hand incorporating just enough flour that it's no longer sticky, and forms a smooth dough. After kneading, shape into a round ball and place back into the greased mixing bowl. Let stand covered with a damp towel in a draft free space for 2 hours or until doubled in size.
Punch down dough and turn out onto a floured surface. Roll about 3/4 inches thick. Cut dough into rounds using a 3 1/2 inch round cutter.
Place onto a greased sheet pan leaving enough space between that they don't touch. Cover loosely with plastic wrap and let rise for 1 hour or until doubled. (You can also cover and chill overnight at this point.)
Fry: Heat 4-6 inches of oil in a deep pot to 365-375°F. Drop doughnut rounds into oil frying for about 2 minutes per side, or just until puffed and golden. Remove to a paper towel lined sheet pan.
Pour 1 cup granulated sugar into a shallow bowl. Gently turn warm doughnuts to coat in granulated sugar.
Fill with Jelly: Using a piping bag fitted with a round tip insert 1 Tbsp jam into the side of each doughnut. (You may dust with more sugar, if desired.)
Serve immediately. Store leftovers in a paper towel lined airtight container at room temperature or chilled for up to 2-3 days.