Step 1

Remove stems from mushrooms and finely chop stems.

Step 2

Heat olive oil in a skillet over medium heat; cook and stir chopped mushroom stems, shallot, and garlic until softened, about 5 minutes. Pour wine into the skillet; cook and stir mixture using a wooden spoon until liquid is evaporated, 1 to 2 minutes. Cool mixture to room temperature, about 10 minutes.

Step 3

Preheat an outdoor grill for medium heat and lightly oil the grate.

Step 4

Brush the olive oil mixture over the top each mushroom and place, top-side up, on a grilling pan. Mix pesto and pine nuts with the mushroom stem mixture together in a bowl; spoon into each mushroom. Sprinkle Italian cheese blend over the filling.

Step 5

Grill mushrooms on the preheated grill until edges are blackened and stuffing is bubbling, about 10 minutes.