Place the first 10 ingredients in a bowl, stirring to mix. Let stand for 5 to 7 minutes to allow the yeast to activate. When the mixture starts to bubble and foam, add the whole wheat, mixing the ingredients with your hands. Add some of the white flour, a little at a time, mixing, until the dough is manageable.
Turn dough out onto a lightly floured work surface and knead, adding the white flour until hands come clean. Insert a clean thumb directly into the dough and count to 5. If your thumb comes out clean with nothing sticking to you, you are through with the kneading. If not, continue kneading and adding flour until the rule of the clean thumb works. Set dough aside in a warm, draft-free area in the kitchen (the top of the refrigerator is a perfect spot). Cover with a tea towel and allow the dough to rest and double in size. This should take about 45 to 60 minutes.
After the dough has risen, knead again for 1 to 2 minutes. Divide into 6 equal pieces and form into balls. Roll out each ball flat and form into pizza rounds about 6 to 8 inches in diameter and about 1/8-inch thick. Top each with some of the pesto, thyme leaves, mushrooms, a sprinkling of oil, sun-dried tomatoes, and goat cheese.
Bake in a preheated 475 degree oven for 20 to 25 minutes, until the crust is golden on the top and bottom.
This recipe yields 12 servings.
Exchanges Per 1/2-pizza Serving: 1 Carbohydrate (1 bread/starch), 1 Fat.
Nutrition Facts: 90 calories (4% calories from fat), 4 g protein, 4 g total fat (1.1 g saturated fat), 12 g carbohydrate, 2 g dietary fiber, 3 mg cholesterol, 152 mg sodium.