In a small bowl, mix together the packet of yeast, 1 cup warm water and 1 teaspoon sugar. Let stand until foamy, about 5 minutes.
In a large bowl, whisk together the 1/4 cup cane sugar, all purpose flour, salt, and baking powder. Add in the yeast mixture and stir until dough starts to come together. Add in the remaining 1/4 cup water and melted buttery spread and stir until combined.
Turn the dough out onto a well floured surface and knead until smooth, for about 5-6 minutes. If dough becomes sticky while kneading, continue adding flour to allow kneading to continue. Transfer dough to a well-oiled bowl. Cover; let rise for about 2 hours, until the size of the dough has doubled.
Make homemade hazelnut-chocolate spread: In a high powdered blender or food processor fitted with a blade attachment, blend all the ingredients together until smooth and creamy. If needed, add a bit more milk to keep the mixture going until blended. (You can store in the refrigerator for up to a month.)
After dough has risen, turn dough out onto counter top. Shape the dough into 2-inch round balls, flattening as you lay them out onto a greased cookie sheet. Allow to rise for 15 more minutes.
Heat the olive oil in a small dutch oven or large skillet over medium high heat (use a candy thermometer, oil should reach 350°F). Make sure the oil isn't too hot or it will start to smoke. Fry the doughnuts in batches, 2-3 at a time for 2 minutes on each side, or until they are golden brown. Using a slotted spoon, transfer doughnuts to a cooling rack lined with paper towels. After all the doughnuts have been fried, roll them in the cup of cane sugar. Poke a hole in one end and pipe the homemade hazelnut-chocolate spread into doughnuts. Serve immediately.