Preheat oven to 300°F. Spray a 10-cup bundt pan with baking spray with flour.
In a large bowl, beat butter and sugar with a mixer at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Add eggs, one at a time, beating well after each addition. Beat in rum extract.
In a medium bowl, whisk together flour, baking powder, nutmeg, salt, baking soda, and cinnamon. Gradually add flour mixture to butter mixture alternately with buttermilk, beginning and ending with flour mixture beating until just combined after each addition. Spoon into prepared pan.
Bake until a wooden pick inserted near center comes out clean, 55 to 60 minutes. Let cool in pan for 15 minutes. Remove from pan, and let cool completely on a wire rack.
In a medium bowl, whisk together confectioners' sugar, milk, and rum until smooth. Pour over cooled cake. Garnish with nutmeg, if desired.