Step 1Slice each apple quarter into 4 to 5 slices. Toss with lemon juice and cinnamon. Set aside.
Step 2Melt 2 tablespoons butter in large nonstick skillet over medium-high heat. Stir in sugar and bring to slow boil, stirring until sugar is dissolved, about 3 to 5 minutes. Add apples, turning to coat both sides. Cook uncovered until tender and lightly brown, about 5 minutes. Remove and set aside.
Step 3Break matzo into large pieces, about 6 to 8 pieces per square. Place in bowl. Heat milk in microwave until warm. Pour over matzo, turning to wet all pieces. Soak just until damp. Drain and set matzo aside.
Step 4Melt remaining 2 tablespoons butter in same skillet, then add matzo pieces. Cook over medium-high heat just until heated through, 3 to 5 minutes. Combine eggs and vanilla in bowl and beat with fork. Pour over matzo and cook until eggs are set, turning often. Return apples to pan and fold in, cooking until apples are heated through. Garnish with powdered sugar if desired.