In a large bowl stir together 1 1/4 cups of the flour, the yeast, and canela. In a small saucepan heat milk, granulated sugar, shortening, and salt just until warm (120 degrees F to 130 degrees F) and the shortening is almost melted, stirring constantly.
Add the heated mixture to the flour mixture. Add egg. Beat with an electric mixer on low speed for 30 seconds, scraping sides of bowl constantly. Beat for 3 minutes on high speed. Using a wooden spoon, stir in enough of the remaining flour to make a soft dough (dough will still be slightly sticky to the touch). Place dough in a greased bowl; turn once to grease surface. Cover bowl. Chill dough for at least 3 hours or up to 24 hours.
Turn out dough onto a lightly floured surface. Cover and let rest for 10 minutes. Roll dough into an 18x12-inch rectangle. Cut dough into thirty-six 3x2-inch rectangles. Cover and let rest for 30 minutes (dough will not be doubled).
Preheat oven to 200 degrees F. In a large deep saucepan or deep-fat fryer heat 2 inches of vegetable oil to 375 degrees F. Fry dough rectangles, two or three at a time, in hot oil about 1 minute or until golden brown, turning once. Drain on paper towels. Keep bunuelos warm in oven while frying remaining dough rectangles. Serve warm. If desired, sprinkle with powdered sugar. Serve with Anise Syrup.
In a small saucepan melt butter over low heat. Add anise seed and canela stick and cook for 2 minutes. Stir in chopped piloncillo, granulated sugar, and whipping cream. Bring to boiling, stirring constantly. Remove from heat; stir in vanilla and orange extract. Strain mixture through a fine-mesh sieve, discarding solids. Stir orange peel into syrup and serve warm. Makes about 1-1/4 cups.