Preheat the oven to 375°F. Rinse the mushrooms to remove any dirt and pat dry. Do not soak.
Remove the stems and scoop out the gills with a small spoon. Arrange the caps hollow side up in a greased 13x9 baking dish or on a baking sheet.
In a medium bowl, combine the softened cream cheese, parmesan, garlic, white and light green scallion parts, Italian seasoning, Kosher salt, and pepper. Beat with an electric mixer until smooth.
Add the crab meat and fold it in just until combined.
Fill each mushroom cap with about 1½ teaspoons of filling. Start with the smaller caps and add a little more to the bigger ones. This amount fills 20 caps.
In a small bowl, stir the crushed Ritz crackers and melted butter together. Dip the top of each stuffed mushroom into the crumbs. Scoop any crumbs that fall into the pan back onto mushrooms with thin topping.
Bake uncovered for 20 to 25 minutes, until the mushrooms are tender and the topping is golden brown. If the tops are not browned by the time the mushrooms soften, broil on high for 2 minutes, watching closely.
Let rest 5 minutes. Transfer to a platter, sprinkle with the dark green scallion tops, add a squeeze of lemon, and serve with extra lemon wedges.