Special equipment: 1-inch and 2-inch round cutters
For the Mexican chocolate glaze: Combine the cream, chile de arbol, cinnamon sticks and star anise in a medium saucepan and bring to a simmer over low heat. Set aside and let infuse for 30 minutes. Remove the spices, return to low heat and bring to a simmer.
Put the chocolate in a medium bowl, pour the warm cream over and let sit for 30 seconds. Add the corn syrup and vanilla and whisk until smooth. Let cool at room temperature until thick enough to dip.
For the red chile peanuts: Combine the peanuts, ancho chile, chile de arbol and cinnamon on a cutting board and chop finely to incorporate. Toss in the brown sugar and spread the mixture in a shallow bowl.
Dip the tops of the plain doughnuts into the chocolate glaze and sprinkle with the chile peanuts. Dust with confectioners' sugar for additional garnish.
Bring the milk to a simmer in a 1-quart heavy saucepan, then remove from the heat and stir in the sugar and salt. Pour into a large bowl and let cool slightly.
While the milk is cooling, dissolve the yeast in 2 tablespoons warm water in a small bowl, stirring. Let stand for 5 minutes.
Stir the yeast mixture into the milk mixture along with the oil, lemon zest and eggs. Stir in 2 1/2 cups of the flour with a wooden spoon to make a very soft dough. Spread 1 cup of the flour on a work surface and put the dough on top, scraping it from the bowl with a rubber spatula. Knead the dough for about 5 minutes, incorporating all of the flour from the work surface and adding just enough additional flour (if necessary); the dough should be slightly sticky. Transfer the dough to an oiled large bowl and sprinkle lightly with additional flour. Cover the bowl with a clean kitchen towel and let the dough rise in a warm draft-free place until doubled in bulk, 1 to 1 1/2 hours.
Turn the dough out onto a floured surface and roll out with a floured rolling pin until 1 inch thick. Cut out rounds with a 2-inch cutter. To make ring shapes, cut out doughnut holes with a 1-inch cutter. Place on a baking sheet, cover the doughnuts with another kitchen towel and let rise in a warm place for 30 minutes.
While the doughnuts rise, heat about 10 cups vegetable oil in a deep 4-quart pot until it registers 365 degrees F on a deep-fry thermometer. Fry the doughnuts 2 at a time, turning once or twice, until puffed and golden brown, 2 to 3 minutes per batch. Transfer to paper towels to drain.
Yield: 16 doughnuts