In a large measuring cup, whisk together warm milk, butter, egg, and vanilla. Set aside.
In an electric mixer fitted with the dough hook attachment, combine 3 cups flour, sugar, yeast, salt, and cinnamon. With the motor running on low, slowly drizzle in the milk mixture and mix until the dough comes together, about 2 minutes.
Add raisins and increase mixer speed to medium and mix until the dough is smooth and elastic, 9 to 10 minutes. After 5 minutes, the dough should clear the sides of the bowl (have pulled away) but stay attached at the bottom. If the dough is sticking to the sides of the bowl, add the remaining flour, 1 tablespoon at a time, until the dough clears the side of the bowl.
Turn out the dough onto a heavily floured surface and shape into a ball. Place in a greased bowl and spray with nonstick cooking spray. Cover the bowl with plastic wrap and let rise in a warm place (80 degrees to 85 degrees, see recipe notes) until doubled in volume, about 2 hours.
Coat a 9-inch x 13-inch baking dish with nonstick spray or line with parchment paper. Turn the risen dough out on to a lightly floured surface and divide into 12 equal pieces. Shape each piece into a tightly formed bun and place in the prepared baking dish, seam side down.
Cover the buns with plastic wrap coated with nonstick spray and let rise in a warm place (80 degrees to 85 degrees, see recipe notes) until doubled in volume and touching, about 1 hour.
Preheat oven 375 degrees. To make the egg wash, whisk together egg and water. Brush gently over the buns. Bake until the buns are deep golden brown and the interiors have reached 190 degrees, about 20 to 25 minutes. Cool completely, at least 30 minutes.