Preheat oven to 375 degrees F. Line an 8×8 square baking pan with parchment paper and set aside.
In a glass liquid measuring cup, make the vegan buttermilk by combining the almond milk and vinegar. Set aside.
In a medium bowl, make the flax egg by combining the ground flaxseed and water. Stir and set aside for 5 minutes to thicken.
In another medium bowl make the crumble. Add the flour, sugar, cinnamon, and cardamom. Stir until combined. Add the melted butter and stir until combined and a sandy/clumpy texture.
In a large bowl, add the flour, baking powder, baking soda, salt, cinnamon, and cardamom. Whisk until well combined.
In the bowl with the flax egg, add the melted butter, sugar, yogurt, vegan buttermilk that you made, and vanilla. Whisk until well combined.
Add the wet to the dry. Stir with a spatula until just combined. Don’t overmix it. Fold in 1 cup of the pears. Careful not to overmix again.
Pour batter into the lined pan. Top with the last 1/2 cup of diced pears. Generously sprinkle crumble evenly all over the top, making sure you use all the crumble (it may seem like a lot, but it’s not). Bake in the oven for 45 minutes or until a toothpick comes out clean and the top is lightly golden.
Let it cool in the pan for 15 minutes, then carefully transfer the cake out of the pan and let it cool on a wire rack. Slice and enjoy! Store leftovers in an airtight container on the counter for up to 3 days.