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1
Preheat oven to 450 degrees F
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2
On a sheet pan, toss squash with a splash of olive oil to coat, and top with a hearty pinch of rosemary, and a sprinkle of salt, pepper, cayenne, and nutmeg. Roast until tender--around 15 minutes.
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3
In a skillet heat about 1.5-2 tablespoon olive oil and 1 tablespoon butter, add onions and cook until just starting to caramelize, then add mushrooms, and finish cooking through until desired state of deliciousness. Salt and pepper lightly.
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4
Combine squash and onion mixture, and season to taste (if needed). Let cool.
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5
For dough: In mixing bowl, dissolve yeast and sugar in warm water. Let stand about 10 minutes. Stir in flour, salt, herbs, and oil. Beat until smooth. Roll into a ball and let rest until ready to assemble.
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6
Punch down the dough and divide in half. On a lightly floured surface, roll out half the dough to a large rectangle. Spread half of the squash mixture across the dough leaving a 1-inch border. Sprinkle half the cheese (jack and parm) over the top. Starting with the long end, roll up the dough into a roll, pinching the edges to seal. Place on a lightly greased baking sheet and repeat with the remaining ingredients. Let the dough rise 10-15 minutes.
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7
Bake (in 450 degree oven) until golden brown, about 20 minutes. Sprinkle each stromboli with additional Parmesan cheese and return to the oven until the cheese is melted, about 5 minutes.
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8
Let rest 10 minutes before slicing.
