In the bowl of a stand mixer or in a large bowl with a hand mixer, combine egg yolks, whole egg and salt. Beat at high speed until thick and pale yellow, about 5 minutes.
Beat in sugar, cream, vanilla extract and rum. Add flour and beat until dough forms, about 5 minutes.
Turn the dough out onto a floured surface. Divide it in half, then cover with plastic wrap and let it rest for at least 20 minutes.
Working with half of the dough at a time, roll out to ⅛-inch thickness. Using a pizza cutter or a sharp knife, cut the dough into 2-inch-wide strips.
Cut the strips on the diagonal at 4-inch intervals. You'll have 2x4 inch rectangles.
Make a slit in the center of each strip of dough. Pull one end through the slit to create the traditional twist shape. (Like a Topsy Tail, if you remember those!)
Heat 2 inches of oil in a large, deep skillet to 350°F.
Fry 4 to 6 faworki at a time for 1 minute or less per side or until golden brown. Keep an eye on them, they fry quickly! Drain the crisped faworki on paper towels.
Dust with confectioners' sugar.