Combine the first seven ingredients (through the flour) in a large mixing bowl. Mix with a sturdy spoon to form a wet dough (it's ok if it's not perfectly smooth). Cover loosely and let rise in a warm place for two hours, or until doubled in size. At this point, the dough can be refrigerated for up to 5 days.

Place a portion of dough on a floured surface; roll to 1/4-inch thickness. Use a 3 inch round cookie cutter to cut out the doughnuts, use a small 1-inch cutter to cut out the center holes (you can also eyeball it and cut the center holes with a sharp knife). Re-roll the scraps or add back to the bowl to use another time. Let doughnuts rest 30 minutes.

Add about 3 inches of oil to a heavy pot. Heat to 350ºF. Drop in the doughnuts, one or two at a time. If the oil is hot enough, they should immediately puff up. Cook for 30 seconds, or until golden brown on the bottom. Flip and cook on the other side for 30 seconds. Remove from the oil and place on a cooling rack set over a few paper towels. Repeat with remaining doughnuts.

Make the glaze by combining the powdered sugar, milk, and honey. Dip the cooled doughnuts into the glaze; immediately press into the chopped peanuts.