Arrange rack in upper third of oven. Preheat oven to 375°F. Lightly butter an 8-by-8-by-2-inch baking pan. In a large bowl, gently mix pears with lemon juice, cinnamon and 1 Tbsp. flour until pears are well-coated. Arrange cut side down in prepared pan.
In a large, resealable plastic bag and with a rolling pin or a meat pounder, crush gingersnaps finely. Transfer crumbs to a bowl. (There should be about 2 cups.)
Stir 1/2 cup flour and sugar into crumbs. Blend in butter, using a fork or fingertips. (Mixture will look damp and feel like coarse sand.)
Sprinkle crumb mixture evenly over pears. Bake until edges are browned and juices just begin to bubble, about 30 minutes. Cool slightly. Serve warm or at room temperature with ice cream, if desired.