In the bowl of a stand mixer fitted with the paddle attachment, beat 1 cup flour, sugar, 1 tablespoon salt, yeast, and baking soda at low speed until combined.
In a small saucepan, heat ¾ cup water, milk, 3 tablespoons butter, and 3¾ teaspoons honey over medium-low heat, stirring occasionally, until butter is melted and mixture registers 125° on an instant-read thermometer. Add milk mixture to flour mixture; beat at medium-low speed until combined, about 1 minute, stopping to scrape sides of bowl. Gradually add 2¼ cups flour, beating on low speed just until combined, stopping to scrape sides of bowl.
Switch to the dough hook attachment. Beat at low speed until a soft, slightly sticky dough forms, 10 to 12 minutes, stopping to scrape sides of bowl and dough hook. (Beat in up to remaining ¼ cup flour, 1 tablespoon at a time, if dough is too sticky.) Turn out dough onto a lightly floured surface, and shape into a smooth round.
Lightly spray a large bowl with cooking spray. Place dough in bowl, turning to grease top. Cover and let rise in a warm, draft-free place (75°) until doubled in size, about 45 minutes.
Punch down dough; cover and let stand for 10 minutes. Spray an 11-cup cast-iron muffin pan with cooking spray. In a small microwave-safe bowl, heat remaining 5 tablespoons butter, remaining 2¼ teaspoons honey, and remaining ½ teaspoon salt on high in 10-second intervals, stirring between each, until melted.
Divide dough in half. On a lightly floured surface, roll half of dough into a 12-inch square. (Keep remaining dough covered to prevent it from drying out.) Brush 1 tablespoon melted butter mixture onto dough. Using a pizza cutter, cut dough into 12 (6×2-inch) strips. Layer 6 strips on top of each other, butter side up; repeat with remaining 6 strips to create another stack. Using a floured serrated knife, cut each stack crosswise into 3 (2-inch) squares. Place each square stack, layers side up, in prepared muffin cups. Repeat procedure with remaining dough and 1 tablespoon melted butter mixture. Slightly separate layers of each roll. Cover loosely with plastic wrap, and let rise in a warm, draft-free place (75°) until dough is puffed and fills cups, 15 to 25 minutes.
Preheat oven to 350°.
Brush beaten egg onto tops of rolls.
Bake until lightly browned, 15 to 17 minutes. Let cool in pan on a wire rack for 10 minutes. Brush rolls with remaining butter mixture; serve warm.
Notes
KITCHEN TIP-This modern recipe makes 12 rolls, but our vintage muffin pan has only 11 cups; we simply baked the remaining roll in another muffin pan alongside the vintage pan.
Recipe by Southern Cast Iron at https://southerncastiron.com/honey-butter-fan-rolls/