Preparation Preheat oven to 350°F. Generously butter twelve 1/3-cup nonstick muffin cups. Divide cornbread cubes and white bread cubes between 2 rimmed baking sheets. Dry slightly in oven, about 5 minutes. Cool. Transfer to large bowl. Melt butter in large skillet over medium heat. Add leeks and celery; cook until soft, stirring often, about 10 minutes. Add ham; stir 1 minute. Add all herbs, 1 teaspoon coarse salt, and 1 teaspoon pepper; stir to blend. Add vegetable mixture to bread; toss. Add eggs and broth; toss. Let stand 5 minutes; toss again. Spoon about 1/2 cup stuffing mixture into each muffin cup. Press to compact. Mound about 1/2 cup remaining stuffing mixture over stuffing in each muffin cup, pressing to hold shape. Bake muffins until golden, about 22 minutes. Cool in pan 15 minutes. Using small plastic knife, loosen muffins. Transfer to rack; cool. DO AHEAD: Can be made 1 day ahead. Cool, cover, and chill. Rewarm uncovered in microwave in 30-second intervals, or covered loosely with foil in 350°F oven, about 15 minutes.
Preparation Preheat oven to 350°F. Generously butter twelve 1/3-cup nonstick muffin cups. Divide cornbread cubes and white bread cubes between 2 rimmed baking sheets. Dry slightly in oven, about 5 minutes. Cool. Transfer to large bowl. Melt butter in large skillet over medium heat. Add leeks and celery; cook until soft, stirring often, about 10 minutes. Add ham; stir 1 minute. Add all herbs, 1 teaspoon coarse salt, and 1 teaspoon pepper; stir to blend. Add vegetable mixture to bread; toss. Add eggs and broth; toss. Let stand 5 minutes; toss again. Spoon about 1/2 cup stuffing mixture into each muffin cup. Press to compact. Mound about 1/2 cup remaining stuffing mixture over stuffing in each muffin cup, pressing to hold shape. Bake muffins until golden, about 22 minutes. Cool in pan 15 minutes. Using small plastic knife, loosen muffins. Transfer to rack; cool. DO AHEAD: Can be made 1 day ahead. Cool, cover, and chill. Rewarm uncovered in microwave in 30-second intervals, or covered loosely with foil in 350°F oven, about 15 minutes.