In stand mixer bowl, add 1 cup flour, yeast, sugar, salt, oats, lemon pepper and cheese; mix well. In saucepan or microwave-safe dish, heat buttermilk and oil to 120-130°F. Add to flour mixture. Using a paddle attachment, beat on medium speed for 3 minutes.
Switch to dough hook attachment. Gradually stir in peppers, onions, zucchini, and enough remaining flour to make a firm dough. Knead until smooth and elastic, about 5 to 7 minutes.(NOTE: For hand mixing: following above steps, mix ingredients in large mixing bowl using a wooden spoon or dough whisk. Knead on floured surface until smooth and elastic.) Place dough in lightly oiled bowl and turn to grease top. Cover; let rise until indentation remains after poking dough with finger down to second knuckle, about 1 hour.
Turn dough onto lightly floured surface; punch down to remove air bubbles. Divide dough in half; let relax 5 minutes. Roll each part into an 8- inch rope. Overlap two ends; twist ropes together. Pinch ends to seal; tuck under. Place in greased 8 x 4- inch loaf pan. Cover; let rise until indentation remains after lightly touching.
Preheat oven to 375°F.
Gently brush risen loaf with 1 teaspoon milk. Bake for 30 to 40 minutes. Remove from pan; cool on rack.