Preheat oven to 375 degree F. In a medium bowl stir together all-purpose flour, whole wheat flour, sugar, baking soda, salt, and pepper. Using a pastry blender, cut in butter until mixture resembles coarse crumbs. Stir in shredded Parmesan cheese and garlic. Make a well in center of flour mixture. Add buttermilk. Using a fork, stir until mixture can be shaped into a ball.
Turn the dough out onto a lightly floured surface. Knead for 8 to 10 strokes or until dough is almost smooth. Divide dough in half. Roll each portion into a 12x9-inch rectangle. Use a pastry wheel or knife to cut rectangles into 3x3-inch squares. Use a fork to prick squares well. Coat the bottom side of a mini-muffin pan with nonstick cooking spray. Lay dough squares over muffin cup bottoms, making sure edges of squares don't overlap. Place inverted muffin pan on a shallow baking sheet.
Bake about 10 minutes or until golden brown. Remove cracker cups from muffin pan; cool on a wire rack. (Cracker cups may be made up to 3 days ahead. Store in an airtight container at room temperature (Or freeze cracker cups in a freezer container up to 3 months).
In a medium bowl toss romaine with salad dressing. To serve, sprinkle some chopped egg in the bottom of each cracker cup. Fill with romaine mixture and top with chopped beet and shaved Parmesan cheese. Makes 24 appetizers.
Preheat oven to 375 degree F. Scrub medium beet; trim off stem and root ends. Peel the medium beet and cut into 3/4-inch pieces or halve the baby beets. Place beets in an 8x8x2-inch baking pan. In a small bowl combine olive oil, garlic, balsamic vinegar, salt, and pepper. Drizzle over beets; toss lightly to coat. Cover pan with foil and roast for 35 minutes. Uncover and roast 10 minutes more or until beets are tender. Cool to room temperature. Chop. Set aside.