Preheat oven to 425°F (220°C). Line two large baking sheets with parchment paper.
Slice all vegetables to a uniform 1/2-inch thickness. Pat eggplant dry with paper towels.
Arrange vegetable slices in a single layer on baking sheets. Brush with olive oil, season with salt, pepper, and oregano. Roast 20–22 minutes, flipping once at 12 minutes, until golden-edged and just tender. Cool 10 minutes. Reduce oven to 400°F.
Combine ricotta, feta, basil, thyme, and garlic in a bowl. Stir well. Taste and adjust seasoning.
Assemble: place one eggplant slice as base. Spread 2 tablespoons herb cheese evenly. Add zucchini, cheese, squash, cheese, tomato on top. Press gently. Make 4 napoleons.
Return to 400°F oven for 10 minutes until cheese is melted and structure has set.
Blend 1/4 cup olive oil with fresh basil and a pinch of salt until smooth and vivid green for basil oil.
Transfer each napoleon with a wide spatula. Drizzle with basil oil, finish with flaky salt. Serve immediately.