In the bowl of the stand mixer and using the paddle attachment, cream together the sugar, salt, and butter, until light and fluffy.
Add the eggs, one at a time, and mix thoroughly. Add the lemon extract/zest and mix until combined.
In the small bowl, stir together the flour and yeast, then add to the butter mixture and stir. Add the milk.
Mix on low speed until the dough starts coming together in a ball and clears the sides of the bowl. Switch to the dough hook, and knead on low for about 10 minutes, until the dough is smooth and supple, not sticky. If the dough is too sticky, add a tablespoon or two of flour. If the dough is too dry and shaggy, add a tablespoon of milk.
Transfer the kneaded dough to the oiled large bowl, and spray a little cooking spray over the top of the dough. Cover the bowl with plastic wrap and set aside in a warm location to rise until doubled, about 2 hours.
Move the dough onto a silicone pastry mat or mist some cooking spray on your work surface, then roll it out into a rectangle about ⅔-inch thick. Lightly dust the top of the dough with flour while you work to keep the rolling pin from sticking. If you want 12 to 16 buns, then make the rectangle 9 inches by 18 inches. If you want 8 buns, then make the rectangle 12 inches by 14 inches.
Sprinkle the cinnamon sugar on top of the rectangle, then roll the dough into a log. Cut the log in half, and then half each piece again. Continue cutting until you have the desired number of buns (8 to 16).
Place the cut buns on the parchment paper with about ½-inch distance between them. Allow the buns to sit at room temperature for up to 90 minutes, until the buns have nearly doubled in size and spread into each other.
Preheat the oven to 350°F (175°C). Put the rack in the middle of the oven.
Bake the buns for 20 to 30 minutes, until golden browned. Remove from oven and allow to cool in the pan for 10 minutes.
While the buns are baking, stir together the powdered sugar, extract, and milk in a small bowl. Whisk until the mixture is smooth and thick.
Drizzle the glaze over the tops of the buns while they are still warm. Remove buns to a cooling rack and allow to sit for 20 minutes before serving.