Generously coat a 4- to 5-quart slow cooker with cooking spray or line the slow cooker with a disposable liner. Add pears to cooker. In a small saucepan combine the 1/2 cup brown sugar, the 1/4 cup butter, and the ginger. Cook and stir over medium-high heat until the butter melts and sugar dissolves. Pour mixture over pears; stir to coat.
In a large bowl beat the 3/4 cup brown sugar and the 1/2 cup butter with an electric mixer on medium speed until thoroughly mixed. Beat in egg. Beat in molasses.
In a medium bowl combine flour, baking soda, cinnamon, baking powder, and salt. Add half of the flour mixture to butter mixture, beating on low until combined. Add chai; mix slightly. Add the remaining flour mixture and beat until combined. Spread mixture evenly over pears in cooker.
Place a clean dish towel over top of slow cooker then top cooker with lid. Cook on high-heat setting for 2 to 2-1/4 hours or until a toothpick inserted in center of the cake layer comes out clean. If possible, carefully rotate crockery liner halfway through cooking time to ensure even cooking.
Remove crockery liner from cooker, if possible, or turn off cooker. Cool on a wire rack for 5 minutes. Remove lid and towel. To unmold cake, run a butter knife around edge of crockery liner. Place a large plate over the crockery liner. Using pot holders, carefully invert cake onto plate. Serve cake warm or at room temperature. If desired, top each serving with yogurt and sprinkle with nutmeg.