For the eggplant cream, preheat oven to 350°F (230 °C).
Lightly brush one eggplant with oil and roast on a foil-lined baking tray for 30 to 35 minutes, rotating every 10 minutes.
In a small saucepan over medium heat, stir together cream, bay leaf, and thyme. Let simmer for about 10 minutes, reducing by half. Strain and reserve cream.
Once eggplant is fork tender, remove from oven and let cool for five minutes. Remove skin and stem, and place eggplant flesh in a blender.
Add infused cream, season with salt, and blend until your eggplant cream is smooth. Adjust seasoning as needed.
For the confit tomatoes, in a medium sauce pot, heat oil over a low heat.
Add tomatoes, garlic and salt, let cook for 35 minutes, making sure the oil never reaches a simmer (oil can be reserved and later used for salad dressings and finishing).
To make the lemon ricotta, in a small bowl, stir together ricotta, cream, lemon zest, salt, and pepper. Mix until smooth, and set aside.
For the fried eggplant rounds, cut the eggplant into 1/3-inch-thick disks. Brush with balsamic vinegar and season with salt. Set aside.
Then, prepare the breading station (flour, whisked eggs, and mixed Italian and panko breadcrumbs) in three separate vessels. First dredge eggplant rounds in flour, making sure to shake off the excess. Next, dip rounds into egg, letting excess drain back into bowl. And finally dip the rounds in the breadcrumb mixture, pressing the breadcrumbs into the eggplant lightly to ensure full and even coverage. Transfer rounds to a plate or baking sheet.
Heat oil in large skillet over medium-high heat. In batches, shallow fry the eggplant until golden brown and crispy, about two minutes per side.
Transfer to a paper towel-lined baking sheet to drain the excess oil. Season with salt, and use remaining oil for crispy capers.
To make the capers, while the oil is still hot, pat capers dry with paper towel and add to oil, frying until crispy, about two minutes. Remove onto paper towel to drain.
For the parmesan crisp, heat a non-stick pan over medium-low heat. Sprinkle a shallow pile of Parmigiano-Reggiano cheese and let melt, untouched, and crisp up until light golden brown. Slide out of pan onto baking sheet and let cool.
To plate, smear a quarter of the eggplant cream onto each plate.
Onto the smear, place a piece of the fried eggplant, followed by a dollop of ricotta and repeat three more times, alternating eggplant and ricotta (for a total of four eggplant rounds per plate).
Surround eggplant with four to five confit tomatoes.
Drizzle with a little of the garlic tomato oil and sprinkle with fried capers.
Break parmesan crisp into four pieces and scatter over each plate. Finish with finely chopped chives.