How to Make It
Preheat oven to 425°F. Lightly grease 16 compartments of 2 (12-compartment) doughnut pans. Toast sesame seeds in a medium skillet over medium, stirring often, until they smell nutty, 2 to 3 minutes. Process until coarsely ground, about 1 minute.
Beat granulated sugar, brown sugar, butter, and oil with an electric mixer on medium speed until smooth. Add eggs, 1 at a time, beating just until combined after each addition. Add baking powder, baking soda, lemon zest, 1 teaspoon of the vanilla, 3/4 teaspoon of the salt, and, if desired, food coloring paste, beating just until combined.
Whisk together flour and 1/2 cup of the ground sesame seeds in a medium bowl. Add flour mixture to sugar mixture alternately with milk, beginning and ending with flour mixture.
Pipe or spoon batter evenly among prepared compartments of doughnut pans. Bake in preheated oven 10 minutes. Remove from oven, and let stand 5 minutes. Transfer doughnuts to wire racks.
Whisk together powdered sugar, milk, lemon juice, 1/4 cup of the ground sesame seeds, and remaining 1 teaspoon vanilla and pinch of salt in a medium bowl.
Dip tops of doughnuts into glaze, and return to racks. Let stand until glaze sets.