Dissolve yeast and honey in 1/4 cup of warm water. In a mixer fitted with a dough hook, combine the flour and salt. Add the yeast mixture and remaining 3/4 cup water and mix on low speed until the dough comes away from sides of bowl (about 5 minutes). Turn dough out onto clean work surface and knead by hand for 2-3 minutes. Dough should be smooth and firm. Cover with a clean, damp towel and let rise in a warm spot for about 30 minutes.
Divide dough into four equal pieces and shape into balls. On a smooth, unfloured surface, roll each ball under palm of hand until top of the dough is smooth and firm, about 1 minute. Cover dough balls with a damp towel and let rest for 15-20 minutes. Place each on a clean, lightly floured surface; press down on center, spreading dough into an 8-inch circle, leaving border thicker than the center. Prick dough about 12 times with a fork and place on pizza stone or heavy non-stick sheet pan.
Heat oven to 500 degrees. Divide apples and mushrooms evenly among the four crusts. Season with rosemary and thyme and sprinkle with cheese. Top pizzas with nuts and cranberries. Bake until cheese melts and begins to brown, about 9-12 minutes. Reduce oven temperature to 300 degrees and continue to bake for 3-4 minutes. Remove from oven and allow to cool slightly. Slice and serve.
Makes 4 eight-inch pizzas.