In a medium bowl whisk the chimichurri ingredients. Set aside until ready to serve.
In a medium bowl mash the avocados. Add the remaining guacamole ingredients and stir to combine. Cover with plastic wrap, pressing the wrap directly onto the surface of the guacamole to prevent it from browning. Refrigerate until ready to serve.
Cut away the stems and any curled edges around the rims of the portabello mushrooms. With a spoon gently scrape away the dark gills that might be holding dirt. Wipe clean. Brush both sides with oil.
Prepare the grill for griddle setup. With the grill in the off position and cool, replace the right-side grate with the griddle. Preheat the grill with the control knob in the medium position for 10 to 15 minutes.
Brush the griddle with oil. Brush the cooking grate clean with a stainless steel bristle grill brush.
Place the mushrooms and shallot halves on the griddle, and cook over direct medium heat, with the lid closed, until tender, turning once. The mushrooms will take 8 to 12 minutes and the shallots will take about 20 minutes. Remove from the grill as they are done. Cut the mushrooms and shallots into thin slices.
Grill the lime halves on the cooking grate, cut side down, until nicely marked by the grill, about 4 minutes. Remove from the grill.
Warm the tortillas on the cooking grate, two at a time, over direct medium heat, for about 30 seconds, turning once. Repeat with the other two tortillas.
Squeeze the juice from the grilled lime into the guacamole and stir to combine.
Wrap up some chimichurri, guacamole, mushrooms, shallots, bell pepper, cabbage, and sprouts inside each tortilla. Serve immediately.
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