Make the dough: Combine 1 cup milk, heated to 115°, with ½ tsp. sugar, nutmeg, yeast, and vanilla seeds in the bowl of a stand mixer fitted with the hook attachment; let sit until foamy, about 10 minutes. Whisk in ¼ cup sugar and egg until smooth; add flour and salt, and mix until dough forms. Increase speed to medium-high, and knead for 4 minutes. While mixer is running, slowly add butter to dough, 1 tbsp. at a time, and mix until smooth; continue kneading for 4 minutes more. Cover bowl with plastic wrap and let dough sit until doubled in size, about 1 hour.
Meanwhile, bring remaining milk, sugar, walnuts, and rum to a boil in a 2-qt. saucepan over medium-high heat, and cook, stirring often, until liquid is reduced and mixture is brown and has thickened, about 15 minutes. Remove from heat, and stir in juice; let walnut mixture cool completely. Punch down dough, and add walnut mixture to dough; return to mixer fitted with the hook attachment, and mix on low speed until walnut mixture is evenly incorporated into the dough. Transfer dough to a greased 8″ x 5 1⁄2″ x 2″ loaf pan and cover loosely with plastic wrap; let sit until slightly risen, about 45 minutes.
Heat oven to 350°. Uncover loaf, and bake until golden brown and an instant-read thermometer reads 190°, about 1 hour, 15 minutes. Let cool completely.