In a large mixing bowl, whisk together the all-purpose flour, granulated sugar, and salt until well combined. Cut in the cold butter until the mixture resembles coarse crumbs. Gradually add ice water until a dough forms. Shape the dough into a disk, wrap in plastic wrap, and refrigerate for 30 minutes to firm up.

While the pastry chills, peel and slice the fresh pears into thin wedges. In a separate bowl, toss the sliced pears with brown sugar, flour, chai spice blend, ground ginger, and ground cardamom until coated.

In another bowl, combine oats, chopped almonds, brown sugar, and melted butter until crumbly. This will serve as the crumble topping.

Preheat the oven to 375°F (190°C). Roll out the chilled pastry dough until it's large enough for a 9-inch tart pan. Transfer the dough to the pan, press it into the edges. Pour the prepared pear filling into the crust and sprinkle the crumble topping over the top.

Place the tart on a baking sheet and bake for 40-50 minutes, until the crust is golden brown and the filling is bubbling. Allow to cool slightly on a wire rack before slicing.