For the sauce: Put 1 1⁄3 cups port, red wine, 2⁄3 cup plum wine, and shallots into a medium saucepan and bring to a boil over medium-high heat. Reduce heat to medium and cook, stirring occasionally, until reduced by half, about 30 minutes. Add stock and cinnamon and cook until liquid has reduced to about 1 cup, about 30–35 minutes. Strain through a fine-mesh sieve and return to saucepan (discard solids). Set aside.
For the garnish: Put 1⁄2 cup port, 1⁄2 cup plum wine, brown sugar, and ginger into a small pot and bring to a boil over medium heat. Reduce heat to medium-low and cook until syrupy, about 35 minutes. Remove from heat and set aside.
For the foie gras and pineapple: Sprinkle granular sugar evenly over tops of pineapple slices and caramelize with a kitchen torch. Set aside in a single layer. Heat oil in a large skillet over medium-high heat. Generously season each piece of foie gras with salt and pepper, then dredge lightly in flour, shaking off any excess. Sear foie gras on both sides until crisp and golden brown, 1–1 1⁄2 minutes per side. Transfer to a paper towel-lined plate.
To assemble: Bring sauce to a simmer over medium heat. Reduce heat to low and whisk in butter a little at a time until smooth and glossy. Place 1 piece of pineapple on each of 4 warm plates and top each with a slice of foie gras. Spoon sauce over foie gras, then top with a dollop of the ginger garnish and some of its syrup. Serve immediately.