Combine boiling water and mushrooms in a bowl; cover and let stand 30 minutes. Drain; discard stems, and mince caps.
Combine mushroom caps, rice, and next 8 ingredients, and stir well.
Working with 1 won ton wrapper at a time (cover remaining wrappers to keep them from drying out), spoon about 1 tablespoon spinach mixture into center of each wrapper.
Moisten edges of wrapper with water, and bring 2 opposite corners to center, pinching points to seal. Bring the remaining 2 corners to center, pinching points to seal. Pinch 4 edges together to seal. Place pot stickers on a large baking sheet sprinked with cornstarch; cover loosely with a towel to keep them from drying out.
Heat 2 teaspoons vegetable oil in a large nonstick skillet over medium heat. Place half of pot stickers in bottom of skillet; cook 3 minutes or until bottoms are lightly browned. Add 1/2 cup water to skillet; cover and cook 3 minutes or until liquid is absorbed. Place pot stickers on a serving platter; set aside, and keep warm.