Grease a 9 x 5 x 3 inch loaf pan with butter and line the bottom with parchment. Warm the milk to about 110 degrees F. Whisk together the yeast and warm milk, then stir in 1 cup of flour until a sticky ball forms. Cover and let rest 20 minutes.

Place the cold butter, sugar, salt, egg, egg yolks, zest, and rum in the food processor. Pulse 5 to 7 times. Scrape in the starter dough and pulse to incorporate. Add the remaining 1 ½ cups flour and process until smooth, about 8 to 10 pulses. Leave the lid on and rest 10 minutes.

While the dough rests, melt the chocolate in a heatproof bowl over simmering water. Remove from heat, stir in baking soda, cinnamon, and water. Set aside to cool slightly.

Pulse the rested dough 10 more times, then turn onto a floured surface. Fold and knead 5 to 6 times until elastic. Divide into 3 equal pieces.

Place one dough piece in the food processor. Add the chocolate mixture and pulse 3 to 4 times to incorporate. Add the 3 tablespoons flour and pulse until smooth. Turn out and knead gently until it holds together. Cover the plain dough pieces while you work.

Press each dough piece into a rough 7-inch square. Stack them with the chocolate dough in the middle. Cut the sandwich into 3 strips, then cut the strips into ½-inch pieces.

Place all pieces in a large bowl, sprinkle with 1 teaspoon of water, and gently toss together. Press and squeeze into a solid ball, adding a pinch of flour if too sticky. Do not overwork. Flatten into a rough 4 x 8 inch rectangle, place in the prepared pan, and press down to fill evenly.

Spread the softened butter over the top. Cover loosely with buttered plastic wrap and let rise for about 2 hours until the loaf rises about 1 inch above the rim of the pan.

Preheat the oven to 350 degrees F about 15 minutes before the rise is complete. Bake for 35 to 40 minutes until the top is deep golden brown. Cool in the pan for 5 minutes, then unmold onto a wire rack. Cool on its side to preserve the shape.