Combine sugar, yeast, lemon zest, and 2 cups flour in mixer bowl.
Fit mixer with flat beater.
Heat butter and milk over low heat until thermometer registers between 120 and 130 degrees.
With mixer running at lowest speed, slowly pour milk mixture into flour mixture.
Increase speed to medium and beat for 2 minutes.
Scrape bowl.
Add eggs, lemon extract, 2 more cups flour, and salt.
Increase speed to medium and beat 2 more minutes.
Scrape bowl.
Change to dough hook.
Add last 3-1/2 cups flour.
Mix until smooth and elastic, about 8-10 minutes.
Place in a large lidded container that has been oiled or sprayed with cooking spray.
Cover and let rise in a warm place until doubled in bulk, about 1 hour.
Divide dough into 1-ounce portions.
Roll each portion into a 12-inch rope.
Lay out 3 ropes at a time.
Pinch together at top and braid. (See photos above.)
When done, pinch bottom together. Flip over, and roll up.
Tuck edge under the bottom and place on parchment paper lined baking sheet.
Let rise until nearly doubled, about 45 minutes to 1 hour.
While dough is rising, preheat oven to 350 degrees.
Place rolls in oven and bake until golden brown, about 15 minutes.
Remove to cooling racks.
When cool, drizzle with lemon glaze.