For the dough: In a medium bowl, mix the yeast with the warm water and let sit for 5 minutes. Add 2 tablespoons olive oil, salt and sugar, and whisk. Set aside.
In a large bowl, mix the all-purpose and whole wheat flours. Make a hole in the middle and pour in the yeast mixture. Slowly hand mix the flour until all the liquid is absorbed. If too wet, add more flour, 1/4 cup at a time. Sprinkle a clean work station with flour and knead the dough until smooth and elastic. Coat a large ceramic bowl with the remaining olive oil. Place the dough in the ceramic bowl and flip over to coat in the oil. Cover the top of the dough with plastic wrap and cover the bowl with a dish towel. Let rise until the dough has doubled in size, 2 hours. Punch down the dough and let rise for another hour.
Heat canola oil to 350 degrees F in a deep-fryer. Dust a clean surface with flour.
Tear small chunks of the dough and roll into sticks. If they get too sticky, toss in flour and roll some more. Deep-fry until crispy and golden, 2 to 3 minutes. Drain on a wire rack.
For the chocolate nougat fondue: Melt the honey nougat milk chocolate over a double boiler on medium-low heat. Add the bittersweet chocolate and whipping cream. Stir until melted. Pour into a bowl.
Put the frittelles on a plate and serve with a side of the chocolate nougat fondue.