Position rack in center of oven and preheat to 375°F Stir butter in heavy small saucepan over medium heat until melted and golden brown, about 3 minutes. Remove from heat.
Stir flour, oats, sugar, rosemary, baking powder, baking soda, salt, and 3/4 teaspoon pepper in large bowl to blend. Pour buttermilk and melted browned butter over flour mixture; stir with fork until flour mixture is moistened.
Turn dough out onto floured work surface. Knead gently until dough comes together, about 7 turns. Divide in half. Shape each half into ball; flatten each into 6-inch round. Place rounds on ungreased baking sheet, spacing 5 inches apart. Brush tops with beaten egg white. Sprinkle lightly with ground black pepper. Using small sharp knife, cut 1/2-inch-deep X in top of each dough round.
Bake breads until deep golden brown and tester inserted into center comes out clean, about 45 minutes. Cool breads on rack at least 30 minutes. Serve warm or at room temperature.
A Tip: You'll get the most tender soda bread by kneading the dough gently and briefly, just until it comes together, like biscuit dough, so the gluten is minimally developed.