Heat your BBQ (or griddle pan) on medium high heat to smoking. Place the plum halves on the hot grill and cook cut side down for 3-4 minutes without moving them. When your plums are grilled, set aside in a bowl to catch the delicious juice.
Meanwhile, make the pistachio pesto by combining parsley, nuts, garlic, lemon zest and juice, olive oil, salt, and pepper in a small food processor and pulsing to combine (alternatively, this can be done in a mortar & pestle for a chunkier, more authentic pesto).
Taste for seasoning, and add a little more olive oil if you’d prefer a looser finish.
When ready to serve, spoon the stracciatella over the base of a shallow dish and top with the char-grilled eggs, the extra juice, dollops of the pesto, another glug of olive oil, a sprinkle of parsley leaves, flower petals and pistachios, serving with lemon cheeks and an extra grind of pepper.
