Combine 1 cup water and porcini in a 2-cup glass measuring cup. Microwave at HIGH 3 minutes. Let stand 10 minutes. Remove mushrooms with a slotted spoon, reserving liquid in cup. Finely chop porcini.
Cut squash into long, 1 1/2-inch wide pieces. Shave into ribbons using a mandoline or vegetable peeler to yield about 6 cups.
Heat a large (14-inch) skillet over medium-high heat. Add oil to pan; swirl to coat. Add cremini, shallots, thyme, and garlic; sauté 9 minutes. Stir in porcini, sorghum, salt, and pepper. Pour in porcini soaking liquid, stopping before grit at very bottom of measuring cup reaches opening. Arrange squash ribbons on top; cover and cook 4 minutes. Gently stir squash into sorghum mixture; cook 2 minutes or until most of liquid evaporates.
Remove from heat. Sprinkle with cheese; gently fold in cheese until it melts. Sprinkle with parsley and oregano, if desired.
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