In a small bowl, gently mash the sardines with a fork, keeping some texture. Add parsley, lemon juice, capers, and olive oil. Mix to combine. Taste and adjust with more lemon juice or olive oil if needed.
In a shallow bowl, whisk together the egg, finely grated Parmesan, and black pepper until smooth.
Heat olive oil in a skillet over medium heat.
Dip each slice of sourdough into the egg mixture, coating both sides without oversoaking.
Transfer to the pan and cook for 2–3 minutes per side, until golden brown with crisp, cheesy edges.
Spoon the sardine mixture evenly over the warm toast.
Layer the heirloom tomato slices on top, folding or arranging for height and texture.
Sprinkle with flaky salt and red pepper flakes. Serve immediately.