Prep the pan and oven. Preheat your oven to 350°F (175°C).
Grease a donut pan well with nonstick spray or butter, making sure to coat the centers so the donuts release easily.
Mix the wet ingredients. In a large bowl, whisk together eggs, milk, sour cream (or yogurt), oil, and vanilla until smooth.
Add the cake mix. Pour the cake mix into the bowl and stir with a spatula until just combined. Avoid overmixing. The batter should be thick but scoopable.
Fill the pan. Spoon the batter into a piping bag or a large zip-top bag and snip a corner.
Pipe batter into each donut cavity, filling about 2/3 full. This helps keep the shape clean and even.
Bake. Place the pan on the center rack and bake for 10–12 minutes, or until the tops spring back when lightly pressed and a toothpick comes out clean.
Cool briefly. Let the donuts cool in the pan for 5 minutes, then transfer to a wire rack. This short rest helps them set and release without breaking.
Make the glaze. In a small bowl, whisk powdered sugar with milk and vanilla until smooth and pourable.
For chocolate glaze, whisk powdered sugar with cocoa powder and milk.
Dip and decorate. Once the donuts are warm but not hot, dip the tops into the glaze, let excess drip off, and set back on the rack. Add sprinkles or toppings right away so they stick.
Let set. Give the glaze 10–15 minutes to firm up. Enjoy fresh, or store as directed below.