Line two sheet pans with parchment and dust lightly with flour. Fit a wire rack over a third sheet pan for glazing. Set a 3-inch donut cutter nearby.
Make the glaze first: In a medium bowl, whisk powdered sugar, milk, honey, vanilla, and salt until smooth and pourable. If too thick, add milk by the teaspoon; if too thin, whisk in a bit more sugar. Cover and set aside; it will thicken slightly while you fry.
Sift together cake flour, cocoa, baking powder, baking soda, salt, instant espresso, and cinnamon into a large bowl.
In a separate large bowl, whisk the sugar and egg yolks vigorously for 1 minute until thick and slightly lightened. Whisk in sour cream and vanilla until smooth. Stream in the melted butter and melted shortening while whisking until fully combined.
Add the dry ingredients to the wet in two additions, folding gently with a spatula just until no dry streaks remain. The dough will be thick and tacky. Scrape onto a lightly floured sheet of parchment, pat into a 3/4-inch-thick slab, and cover with another parchment sheet.
Chill the sandwiched dough for 25 minutes in the refrigerator, then slide it into the freezer for 8 minutes to firm the surface for cleaner cuts.
While the dough firms up, heat 2 inches of oil in a heavy pot to 350°F (175°C). Adjust the heat to maintain 345–355°F throughout frying.
Peel away the top parchment, lightly flour the dough, and roll to an even 1/2 inch thick. Cut out donuts, dipping the cutter in flour between cuts. Transfer the rings and holes to the prepared floured pan. Gently press scraps together and repeat, avoiding overworking.
Fry 2–3 donuts at a time: slide into the oil and cook about 1 to 1 1/2 minutes per side until the crust is set and the donuts look slightly puffed and matte. Fry holes for about 60–75 seconds total, moving them frequently.
Use a slotted spoon to transfer donuts to the rack to drain for 2 minutes. While still warm (not hot), dip the smooth side of each donut into the glaze, let excess drip back, then return to the rack glazed-side up. For an extra-thick finish, dip a second time after 10 minutes.
Tip: Fry a single donut first to gauge timing and color. If it browns too quickly, reduce the heat; if it takes longer than 3 minutes total, raise the heat slightly.