In a small bowl, combine 2 tablespoons brown sugar with yeast. Add 1/2 cup warm water; stir until yeast dissolves. Let mixture stand 10 minutes until foamy.
Meanwhile, in a large bowl or bowl of a stand mixer fitted with dough hook attachment, stir flour, salt, cinnamon and remaining 2 tablespoons brown sugar until combined. Add yeast mixture along with 1/4 cup warm water, maple syrup, vanilla and 1 egg. Stir until a dough forms.
Knead dough in stand mixer on medium speed 5 minutes, adding just enough of remaining 1/4 cup warm water until dough is smooth, elastic and only slightly sticky; OR, knead dough by hand on a lightly floured surface 10 to 15 minutes, adding just enough of remaining 1/4 cup warm water until dough is smooth, elastic and only slightly sticky. Shape dough into a ball and place in a large bowl. Cover with plastic wrap and let rise in a warm place 1 to 1½ hours until doubled.
Punch down risen dough; let rest 10 minutes. Meanwhile, fill a large, wide pot two-thirds full with water. Heat water to just below a simmer. Heat oven to 425°F, and line a baking sheet with parchment paper or a silicone mat.
Divide dough into 8 equal pieces. Shape each piece into a smooth ball. Use fingers to poke a hole in center of each ball, stretching each hole until it is as big as half the diameter of entire bagel (it might look too big at first, but it will shrink when you boil/bake it). Place bagels on prepared baking sheet. Cover with a damp towel or lightly greased plastic wrap and let rest 10 minutes.
Once bagels have rested, use a slotted spoon to lower a few bagels at a time into simmering water. Allow bagels to float to top. Leave bagels in water 1 to 2 minutes, then flip over and leave in water another 1 to 2 minutes (the longer they stay in the water, the chewier they become). Remove bagels with slotted spoon and return to prepared baking sheet. Repeat with remaining bagels.
Beat remaining egg with 1 tablespoon water, then brush egg wash over tops of bagels. Mix cinnamon and sugar together in a bowl. Sprinkle mixture over bagels.
Bake 20 to 25 minutes until bagels are golden brown and baked through. Remove from oven and let cool completely on a cooling rack before slicing.