Heat the milk, butter, and salt in a medium saucepan over medium-high heat, stirring frequently, just until steam begins to curl from the surface and bubbles form around the edges, about 5 minutes. Set aside to cool until lukewarm.
Meanwhile, in a small bowl, dissolve the yeast and 1 teaspoon sugar in the warm water. Let stand until foamy, about 10 minutes.
In the bowl of a stand mixer fitted with the paddle attachment or with a hand mixer in a large bowl, beat the remaining 1/3 cup sugar and the eggs on medium-high until thick and luscious looking, about 5 minutes. Switch to the dough hook, add the milk mixture, the yeast mixture, and the flour, and mix on low speed until a soft dough forms, about 7 minutes, adding more flour if needed. The dough should be just slightly tacky but not sticky.
Turn the dough onto a lightly floured work surface, shape into a ball, and place in a lightly buttered bowl. Cover with plastic wrap and let rise in a warm, draft-free spot until double in size, about 2 hours.
Lightly coat a 13-by-18-inch rimmed baking sheet with cooking spray and turn the dough onto the pan. Press and poke it with your fingers, much like making focaccia, to help stretch it until it’s about 1/2 inch thick. Lightly coat the top of the dough with cooking spray, loosely cover the pan with plastic wrap, and let the dough rest until double in size, 1 to 1 1/2 hours.
Make the cinnamon sugar
Mix together the sugar and cinnamon in a shallow bowl.
Fry the doughnuts | malassadas
Fill a medium saucepan with 3 inches of oil and heat over medium-high heat until it reaches 350°F (177°C) on a deep-fry or candy or instant-read thermometer. Monitor the heat to keep a steady temperature. Using scissors or your hands, cut or pull a 2-to-3-inch piece of dough from the baking sheet and stretch it into a 4-to-5-inch circle, then lower it into the oil and fry, turning it frequently, just until golden brown on both sides and cooked through, 45 seconds to 1 1/2 minutes, depending on the size. Drain the doughnut on paper towels for 30 seconds and then toss in the cinnamon sugar. Repeat with the remaining dough. Devour warm