Combine mole paste and water in a small saucepan. Bring to a boil, whisking until dissolved. Remove from heat. 

Combine flour, baking powder, and salt in a large bowl. 

Combine vegetable oil, membrillo, and eggs in the bowl of a mixer fitted with the paddle attachment. Beat until smooth, about 3 minutes,  stopping to scrape down the sides. 

Add mole sauce and mix until combined. Then add flour mixture and beat until incorporated. Dough will be very sticky. 

Line two baking sheets with parchment paper and generously sprinkle both with flour. Scrape dough onto one baking sheet, sprinkle with flour, and press until it's about 1/2-inch thick. Place in freezer until firm, about 20 minutes. 

Meanwhile, combine sugar and cinnamon for the topping. 

Cut dough into donuts using either a 3-inch donut cutter or a 3-inch biscuit cutter and a 1-inch biscuit cutter for the middle (aka donut holes). Place donuts (and holes) on the second baking sheet. It should make a dozen donuts on the first cutting. You can re-roll the scraps for more donuts. Place in fridge to rest another 20 minutes. 

Heat 6 cups of vegetable oil over medium-high heat until oil reaches 350°F on a deep-fry thermometer. Carefully place a few donuts at a time into the hot oil—don't overcrowd. Monitor the oil's temperature adjusting it up or down to maintain the 350°F. Fry for 2 minutes per side and then transfer to a paper towel-lined baking sheet. 

Let cool for about 30 seconds then toss in cinnamon-sugar. Repeat with remaining donuts and donut holes.