Combine 1 cup butter and sugar in a large bowl; beat with an electric mixer until smooth and creamy. Mix in molasses and egg until combined.

Mix together buttermilk and 2 teaspoons baking soda in a small bowl. Mix vinegar with remaining 1 teaspoon baking soda in another small bowl. Add the buttermilk mixture to the molasses-egg mixture. Then add vinegar mixture, cinnamon, cloves, ginger, nutmeg, and salt; mix until well combined.

Gradually stir in 4 cups flour, 1 cup at a time, stirring until the dough comes together and forms a ball. Shape dough into a ball, wrap in plastic wrap, and place in the refrigerator until chilled, about 30 minutes.

Preheat the oven to 350 degrees F (175 degrees C).

Place chilled dough on a floured surface and roll to 1/2-inch thickness. Cut out cookies with desired cookie cutters and place on ungreased cookie sheets.

Bake in the preheated oven until edges are golden, about 10 minutes. Cool on the baking sheet for 1 minute before removing to a wire rack to cool, 8 to 10 minutes more.

While cookies are cooling, place 3 cups powdered sugar, softened butter, orange zest, and 1/3 cup orange juice in a bowl. Discard remaining orange juice, or save for another use. Beat frosting ingredients with an electric mixer until consistency is similar to fondant or modeling dough, adding more powdered sugar, if necessary. Frost cookies.