To activate the yeast, combine warm water, Turbinado sugar, and yeast in stand mixer bowl. Cover with a clean kitchen towel for 5 minutes. The yeast should be bubbling at this point.
Add the egg, oil, vinegar, salt, all-purpose flour, and whole wheat flour to the mixer. Combine with a spatula briefly.
Attach your dough hook, and turn on the mixer to a medium speed. Knead the dough for 6 minutes. It should be soft but not sticky at this point.
Grease a large bowl with baking spray or canola oil. Transfer the dough from the mixer to the greased bowl.
Place a clean kitchen towel or plastic wrap over the bowl, and let it proof for 1 hour in a warm place, or until doubled in size.
Grease an 8.5×4.5 loaf pan with baking spray.
Spray a large amount of baking spray in a 12×10 on your counter. Now place the risen dough in the middle of this section. Take a rolling pin and spray that too. Start rolling out the dough about 10 inches in width and 12 inches in length.
Evenly spread the jam across the flattened dough. Leave a 1/2 inch border, so it does not spill out when baking. Now roll it up width-wise. Pinch the seam together and tuck in the sides.
Place the dough loaf into the baking tin and cover with a kitchen towel or plastic wrap. Let it proof for 45 minutes, or until it rises a 1/2 inch above the sides
Preheat the oven to 350 degrees F.
Bake the loaf in the preheated oven for 25 minutes, or until the top is golden and it sounds hollow when you tap it.
Let the bread cool in the pan for 10 minutes, then remove it and place it on a wire rack or large plate to finish cooling.