Preheat the oven to 350 degrees. Coat a 9" round cake pan with cooking spray and set aside.
Rub the sweet potatoes with a few drops of oil or a touch of cooking spray. Place the potatoes on the oven rack and bake until they are soft when squeezed, 40-60 minutes. Remove the sweet potatoes and set aside until cool enough to handle.
Meanwhile, in a small saucepan over medium heat, melt the butter with the brown sugar. Pour the mixture into the prepared pan, tilting to coat the bottom evenly. Arrange six pineapple slices in a ring around the edge and one in the center of the pan.
Peel the potatoes and place the flesh in a mixing bowl. Mash roughly with a fork. Add the eggs, cinnamon, baking powder, salt and 5-6 grinds pepper, and whisk until well-blended. Spoon the mixture into the baking pan, spreading it evenly over the pineapple and smoothing the top. Tap the pan sharply on the countertop three or four times to knock out air bubbles.
Bake until the top looks dry and feels springy to the touch, 40 minutes. A knife inserted in the center should come out clean. Cool in the pan on a rack for 10 minutes. Run a knife around the side of the pan. Insert a serving plate over the pan and, holding the pan and the plate firmly with oven mitts, flip them so the potatoes drop on to the plate, pineapple side up. Lift off the pan. Serve warm.