Preheat the oven to 450 degrees F.
For the biscuits: Add both flours, sugar, baking powder, chai spice, cinnamon, nutmeg, allspice and salt in the bowl of a food processor. Sprinkle with both extracts and pulse to combine. Add the butter and shortening and pulse 6 to 8 times until the mixture resembles coarse meal. Add the ice water, 1 tablespoon at a time, pulsing until the dry ingredients are just moistened. Remove the dough from the processor bowl, flatten into a disk shape, wrap tightly with plastic wrap and refrigerate for 30 to 40 minutes.
For the cream: Whip the cream cheese and yogurt in a medium bowl with an electric mixer until light and fluffy. Beat in the sugar, fresh ginger, crystallized ginger and both extracts until evenly combined. Cover with plastic wrap and refrigerate until serving.
For the cobblers: Add the mangoes, strawberries, blueberries, lemon juice, cornstarch, sugar and mint to a large bowl and stir to combine. Lightly spray 6 (8-ounce) baking bowls with cooking spray. Evenly divide the fruit mixture into the bowls and arrange on a rimmed baking sheet.
Roll out the reserved dough, on lightly floured marble or a flat surface, to 1/4-inch thickness. Cut the dough into 6 rounds or decorative shapes slightly smaller than the width of the bowl. Put 1 piece of dough on top of each cobbler. Brush the dough evenly with egg wash.
Bake the cobblers for 20 minutes, then reduce the heat to 350 degrees F. Bake until the pastry is lightly browned and the fruit is tender and bubbling on the edges, about 5 to 7 minutes longer. Remove from the oven and transfer the bowls to a wire rack. Let cool for 20 to 25 minutes before serving.
Dollop ginger cream on each cobbler and sprinkle with toasted almonds. Garnish with mint sprigs, if desired, and serve.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.