In the bowl of a standing electric mixer fitted with the dough hook, combine the yeast with 1/4 cup of the warm water and the sugar and let stand for 5 minutes. Add the remaining 1/2 cup of water, the whole-wheat and all-purpose flours, the salt and the 2 1/2 teaspoons of olive oil and beat at medium speed until a soft, supple dough forms, about 8 minutes. Roll the dough into a ball, rub it with olive oil and return it to the bowl. Cover the dough and let stand until doubled in bulk, about 1 hour.
Preheat the oven to 500° and place a pizza stone on the bottom rack of the oven, allowing at least 30 minutes for it to preheat. Punch down the dough and divide it into 3 pieces; form them into 3 balls and transfer to a lightly oiled baking sheet. Cover with oiled plastic wrap and let stand for 20 to 30 minutes.
In a large skillet, heat the canola oil. Add the onions and thyme and season with salt and pepper. Cover and cook over moderate heat, stirring once or twice, until the onions soften, about 5 minutes. Uncover and cook until the onions are very soft and golden, about 15 minutes longer; add water as needed to keep the onions from scorching. Discard the thyme.
Spread the the pine nuts in a pie plate and toast in the oven until golden, 2 minutes.
In a large bowl, combine the garlic and olive oil. Add the radicchio, kale and sage, season lightly with salt and pepper and toss.
Turn the broiler on. Roll or stretch one ball of dough to a 10-inch round and transfer it to a floured pizza peel. Mound one-third of the greens on top, followed by one-third each of the onions, pine nuts and cheese. Carefully slide the pizza onto the hot stone and bake until the crust is browned and the toppings are sizzling, 8 to 10 minutes. Cut the pizza into wedges and serve right away. Repeat to make the remaining 2 pizzas.
Nutrition data accounts for one-half pizza.