1. In the bowl of a standing mixer or another large bowl, stir yeast into 1/4 cup warm (110°) water. Let stand until foamy, about 10 minutes. With a wooden spoon, stir in sugar, milk, and eggs (or beat in with paddle attachment); stir or beat in 2 3/4 cups flour, salt, and cardamom (dough will be soft and sticky). Stir or beat in butter, a few chunks at a time, until well incorporated.
If using a mixer: Continue to beat at medium-low speed until dough pulls from sides of bowl, 4 to 5 minutes; add up to 1/4 cup more flour if necessary. Scrape dough down if it crawls up beater or sides of bowl. Remove beater and scrape clean. Scrape dough onto a well-floured board and knead briefly to bring together.
If mixing by hand: Scrape dough onto a lightly floured board and knead until smooth and velvety, about 5 minutes, adding more flour as needed to prevent sticking.
2. Return to bowl, cover with plastic wrap, and let stand in a warm place until dough has doubled, 1 1/2 to 2 hours.
3. Scrape dough onto lightly floured board and press gently to expel air. Divide into 24 equal pieces. With floured hands, divide each piece in half. Form each half into a rope about 4 inches long and 1/2 inch thick. Twist the two ropes together, pinching ends together. Place twists about 1 inch apart on a floured baking sheet and cover with plastic wrap. Let rise until nearly doubled in size, about 30 minutes.
4. Meanwhile, fill an electric deep-fryer to the fill line or pour about 4 inches of oil into a 5- to 6-quart pan and heat to 375°. With a wide spatula, gently slide two twists into oil, one at a time. Cook, turning once, until golden brown on both sides, about 3 minutes total. With a slotted spoon, transfer to paper towels to drain. Repeat to fry remaining twists.
5. When cool enough to handle, dip top half of warm twists in maple glaze. Place on a plate or rack and let stand until glaze is set, about 2 minutes.
Maple glaze: In a bowl, mix 1 cup powdered sugar, 1/2 cup maple syrup, and 1 tablespoon milk until smooth.
Nutritional analysis per twist.