Preheat oven to 350 (175 C) degrees. Butter a 12-cup Bundt cake pan and lightly dust with flour.
Stir together the flour, baking powder and salt in a large bowl until combined. Remove 1 ¾ cups of this mixture to a second bowl and stir in the pumpkin pie spice and ginger. Stir the cocoa into the remaining flour in the first bowl.
Beat the butter in a stand mixer until creamy. Add the sugars and beat on medium-high speed until fluffy. Beat in the eggs, one at a time. Scrape out ½ the batter into another bowl and set it aside.
To make the pumpkin batter
Add the pumpkin to the batter in the mixing bowl and beat briefly on slow speed to blend. (FYI, the batter might appear curdled at this point, but that’s fine – it will come together when you add the flour). Stir in the spiced flour mixture until just blended.
To make the chocolate batter
Stir the reserved butter mixture into the cocoa mixture, alternating with the yogurt, until just blended.
Spoon half the pumpkin batter into the pan. Drop half the chocolate batter by spoonfuls over the pumpkin batter, without covering it completely. Repeat with the remaining pumpkin and chocolate batters. Put a small, thin knife into the batter and circle it around the pan a few times, then draw the knife back and forth across the width of the pan to swirl the batters together.
Bake about 1 hour, or until a tester emerges with a few moist crumbs. Cool the cake in the pan 15 minutes before inverting onto a rack to cool completely.
Put all ingredients for the glaze in a heatproof bowl set over a saucepan of simmering water until melted, stirring until smooth. Pour the glaze over the cool cake, letting some drip over the sides. Let stand until the glaze sets before serving, about 1 hour, or chill for 30 minutes if you’re in a hurry.