Preheat oven to 350°F. Place dried plums and water in a medium saucepan; bring to a boil over medium-high. Cover and reduce heat to medium-low; simmer 5 minutes. Drain. Let cool 20 minutes. Chop plums.

Beat butter in a stand mixer fitted with a paddle attachment on medium speed until creamy, about 1 minute. Gradually add sugar, beating well. Add egg; beat well.

Stir together buttermilk and baking soda in a small bowl. Stir together cinnamon, salt, and 2 cups of the flour in a separate bowl; add to butter mixture alternately with buttermilk mixture, beginning and ending with flour mixture, beating on low speed until combined, about 1 minute. Stir in chopped plums, lemon zest, and vanilla. Toss together pecans and remaining 1/4 cup flour in a small bowl; stir into batter.

Pour batter into a greased and parchment paper-lined 9- x 5- x 3-inch loaf pan. Bake in preheated oven until a wooden pick inserted in center comes out clean, 55 minutes to 1 hour, 5 minutes. Cool in pan 10 minutes. Remove from pan. Transfer to a wire rack; let cool completely, about 1 hour.