Prepare Eggs: Boil eggs for 4 to 4.5 minutes for soft-boiled texture. Cool immediately in water to stop cooking.
Make Cheese Spread: Combine cream cheese, feta, oregano, and pepper. Mix well.
Prepare Aromatic Butter: Melt butter and sauté garlic and chili pepper. Season with salt.
Toast Bread: Butter bread slices and toast until golden.
Assemble Platter: Spread cheese mixture on platter, add toasted bread, and top with soft-boiled eggs cut in half. Drizzle with aromatic butter and garnish with arugula.