In a small bowl, combine warm water, yeast, and a pinch of sugar. Leave for 5 to 10 minutes until the yeast is activated, and you can start to see some bubbling.
Transfer yeast to a bowl of a stand mixer. Add milk, sugar, salt, vanilla, egg, oil, and 2 cups of flour. Mix on low with the dough hook attachment for 2 to 3 minutes. Add the remaining flour and continue to mix for 5 to 8 minutes. Dough should be smooth and elastic.
Transfer dough to a lightly oiled bowl and cover. Allow dough to double in size, about 1 hour.
Knock dough down and re-mould into a large ball. Let dough rest for 5 minutes.
Heat oil to 385F in a deep fryer or large pot.
Preheat grill to 400F.
Tear off golf ball-size pieces of dough. Lightly dust your work surface with flour and roll the dough balls into thin ovals. Lay
rolled out dough on a sheet pan covered with a towel while you finish rolling out the remainder of the dough.
Fry the dough one oval at a time until dough is golden brown on both sides, approx. 3 minutes per side.
Remove dough from the oil with tongs and place on paper towel to drain.
In a large bowl with cinnamon and sugar, toss the beavertail, shaking off any excess.
Grill sausages per package instructions.
Slice grilled sausages on a bias.
Place fried dough on a platter, top with sliced sausages, and drizzle generously with maple syrup.