In the bowl of a stand mixer fitted with the paddle attachment, stir together 1½ cups flour, sugar, salt, and yeast.
In a medium saucepan, heat ⅓ cup water, milk, and butter over medium heat until an instant-read thermometer registers 120° to 130°. Add warm milk mixture to flour mixture, and beat at medium-low speed until combined. Add eggs; beat at medium speed until combined. With mixer on low speed, gradually add 2½ cups flour, beating just until combined and stopping to scrape sides of bowl as needed.
Switch to the dough hook attachment. Beat at low speed until a soft, slightly sticky dough forms, stopping to scrape dough hook and sides of bowl as needed, 12 to 14 minutes. Add up to remaining ¼ cup flour, 1 tablespoon at a time, if dough is too sticky.
Lightly spray a large bowl with cooking spray. On a lightly floured surface, shape dough into a smooth round. Place dough in bowl, turning to grease top. Cover and let rise in a warm, draft-free place (75°) until doubled in size, 30 to 45 minutes.
Recipe by Taste of the South at https://tasteofthesouthmagazine.com/sweet-roll-dough/