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1
Prepare a med-hot fire in a charcoal grill with a cover; or preheat a gas grill to medium-high.
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2
To make the mayonnaise: in a small bowl, mix together the mayo and sun-dried tomatoes; cover and refrigerate until ready to serve.
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3
To make the spice mixture: combine all the spice mixture ingredients in a small bowl; set aside.
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4
To make the grilled portobellos: Combine Zinfandel, olive oil, lemon zest, and 1 tablespoon spice mixture in a shallow bowl; whisk to blend well.
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5
Add in the mushrooms and turn to coat with the marinade; set aside.
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6
To make the patties: combine the ground chuck, Zinfandel, shallots, cumin, cayenne, and remaining spice mixture in a big bowl.
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7
Handling the meat as little as possible to avoid compacting, mix well.
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8
Divide the mixture into 4 equal portions; form portions into patties to fit the rolls.
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9
Drain mushrooms, reserving the marinade.
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10
When the grill is ready, brush grill rack with vegetable oil.
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11
Place the patties and the mushrooms on the rack, cover, and cook, turning once, until the patties are done to preference5 to 7 minutes per side for medium, and the mushrooms 6 to 10 minutes or until tender; brush the mushrooms frequently with marinade.
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12
During the last few minutes of cooking, place the rolls, cut side down, on the outer edges of the grill to toast lightly.
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13
To assemble: spread the mayonnaise over the cut sides of the rolls.
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14
On each roll bottom, place 4 arugula leaves, a patty, 2 tablespoons of the goat cheese, and a mushroom; add roll tops and serve.
