1. Heat olive oil in a large saute pan over medium heat. When oil is hot, add the chopped onion. Cook, stirring occasionally, until translucent, about 6 minutes. Remove pan from heat; set aside until cool.

2. In the detached bowl of an electric mixer, whisk together yeast, 1/4 cup warm water (105 degrees), and a pinch of sugar. Set aside until mixture is foamy, about 6 minutes.

3. Attach bowl to electric mixer fitted with the dough-hook attachment. On low speed, add yogurt, onions, salt, caraway seeds, pepper, eggs, and rye flour. Slowly add enough all-purpose flour to make a soft but not sticky dough. Knead on medium-low speed until dough springs back when pressed with a finger, about 6 minutes. Brush the inside of a large mixing bowl with olive oil. Transfer dough to bowl; cover with oiled plastic wrap. Set aside to rise until doubled in size, about 2 hours.

4. Sprinkle three large baking sheets with cornmeal. Using a kitchen scale, divide dough into 2-ounce pieces. Roll each piece into a 12- to 14-inch length, and make each into a U shape. Cross the end of the U, and then fold crossed ends so they are draped over bottom of the U. If desired, snip each end for a cleaner shape.

5. Place pretzels, 1 to 1 1/2 inches apart, on prepared baking sheets. Cover with oiled plastic wrap, and let rise until almost doubled in size, about 25 minutes.

6. Heat oven to 350 degrees. Whisk together remaining egg yolk and 1 tablespoon water. Brush tops with mixture; sprinkle with salt. Bake until golden, 20 to 25 minutes. Cool at least 5 minutes before serving.