Preheat oven to 350 F. Grease a 9-inch round cake pan with butter.

In a bowl, using a wooden spoon, vigorously beat the 5 Tbs butter , the brown sugar, and maple syrup until thoroughly blended. Spread this mixture over the bottom of the prepared cake pan.

Peel, halve and core the pears, and then cut them into 1/4 inch longitudinal slices. Add the pears to a bowl; sprinkle with the 1 Tbs granulated sugar, the cinnamon, cardamom, and cloves and toss gently to coat. arrange them in the bottom of the pan, fanning and overlapping them slightly, so that the tapered ends point outwards; use the small slices to fill any holes.

In a bowl, whisk together the flour, baking powder, and salt. pour the milk and vanilla into a liquid measuring cup.

Using a stand mixer on medium -high speed, beat the remaining 1/4 cup of butter with the 3/4 cup granulated sugar until light and fluffy, 1-2 minutes. 

Beat the eggs , 1 at a time , scraping the side of the bowl after each addition. 

Reduce the mixer speed to low and add the dry ingredients in 3 batches, alternatively with the milk mixture in 2 batches. raise the mixer speed to medium-high and beat for 2 minutes to aerate.

Scrape the batter into the cake pan and spread evenly. Bake until a cake tester inserted into the center comes out clean, 60-70 minutes.

Immediately place a larger plate, at least 10 inches in diameter, upside down on top of the cake. Carefully invert the cake with the plate, then lift off the pan, gently shaking the pan if necessary to release the cake. let cool at least 30 minutes, then cut into wedges and serve.