Heat a large nonstick skillet over medium-high heat. Arrange mushroom caps, stem sides up, in pan; cook 5 minutes, shaking pan occasionally. Turn mushrooms over; cook 5 minutes, shaking pan occasionally. Place mushrooms, stem sides down, on paper towels to drain and cool.
Place 4 tablespoons pepitas, parsley, and next 7 ingredients (through garlic) in a food processor; process until chopped. With processor on, slowly pour oil through food chute; process until well blended.
Fill each mushroom cap with about 1 teaspoon pesto; top evenly with remaining 2 tablespoons pepitas.