Cut the eggplant into even 1.5 cm cubes. Toss with 1 tbsp fine salt in a colander set over a bowl or the sink, and let drain for 30 minutes, pressing occasionally to release the bitter liquid.
Rinse the cubes briefly under cold water, then pat very dry with kitchen towels. Wet eggplant will steam instead of browning in the pan.
Heat 3 tbsp olive oil in a 12-inch / 30 cm skillet over medium-high until shimmering. Add half the eggplant in a single layer and cook 6 to 7 minutes, stirring occasionally, until deep golden on the edges and tender at the center. Remove and repeat with the second batch, adding more oil if the pan looks dry.
Lower the heat to medium, add the remaining 2 tbsp oil and the garlic. Cook 30 to 45 seconds, stirring, until fragrant but not browned.
Add the cherry tomatoes and a pinch of salt. Cook 5 to 6 minutes, mashing lightly with the back of a spoon, until they collapse into a chunky sauce.
Return all the eggplant to the skillet along with the vinegar and chili flake, if using. Toss to coat and simmer 4 to 5 minutes until the eggplant is fully tender at the center with no raw white left, and the sauce clings rather than pools.
Take the pan off the heat and stir in the basil and parsley. Taste and adjust salt and pepper.
Let it rest 5 to 10 minutes before serving warm, or cool fully to serve at room temperature.