2 medium leeks, light green parts only, minced
4 sprigs fresh thyme, leaves only
2 cloves garlic, minced
⅓ cup dry bread crumbs, divided
⅓ cup all-purpose flour, divided
¼ cup shredded sharp Cheddar cheese
¼ cup shredded Havarti cheese
⅓ cup milk
2 large eggs, divided
½ teaspoon mustard powder
1 teaspoon milk
¼ cup vegetable oil for frying
Pour 1 tablespoon oil into a deep pan and heat over medium heat. Add leeks and saute until tender and fragrant, about 5 minutes. Add thyme and garlic; saute for another 30 seconds. Transfer to a mixing bowl and place in the refrigerator until cooled to room temperature, 20 to 30 minutes. Remove from the refrigerator and add 1/2 of the bread crumbs, 1/2 of the flour, the Cheddar cheese, Havarti cheese, 1/3 cup milk, 1 egg, and mustard powder. Mix until a dough forms. Move to the refrigerator until cooled and congealed, about 30 minutes. Whisk the remaining egg and 1 teaspoon milk together in a bowl. Add remaining flour to another bowl. Place remaining bread crumbs in a third bowl. Roll a handful of the leek mixture into the shape of a sausage. Roll in the flour, coat in the egg wash, then dredge it in the bread crumbs. Repeat to form remaining "sausage" links. Heat 1/2 to 3/4 inch of oil in the same pan over medium-high heat to 350 degrees F (175 degrees C). Fry each link in the hot oil until the outsides are crispy and golden brown, about 2 minutes per side, working in batches if needed. Transfer to a paper towel-lined sheet to drain grease.