Place half of the diced eggplant onto a paper towel-lined microwave-safe plate. Microwave on high for 6 minutes. Place the remaining eggplant onto a second paper towel-lined microwave-safe plate while the first batch is in the microwave. As soon as the first batch comes out, place the second batch into the microwave and repeat, zapping it on high for 6 minutes.
Coat the bottom of a large skillet with the olive oil and place it over medium heat. Give the oil a minute to heat up. Once it begins to shimmer, add the eggplant. Cook the eggplant for about 10 minutes, flipping the pieces every three minutes or so, until they are tender and lightly browned.
Add the shallot to the skillet. Cook it with the eggplant for about five minutes, stirring occasionally.
Push the eggplant and shallots to the side, then add the garlic to the space you just created. Sauté the garlic for about 1 minute, stirring constantly, until it becomes very fragrant.
Stir the garlic into the eggplant and shallot mixture, then stir in the wine. Bring the wine to a simmer and let it cook until reduced by about half, about 4 minutes.
Stir in the tomato sauce and sugar. Bring the sauce to a boil, then lower the heat so that it's cooking at a low simmer. Let it continue to simmer for about 10 minutes, until thickened slightly. You can add a splash of water if it becomes too thick.
Remove the skillet from heat. Season the ragù with salt and pepper to taste. Stir in the basil.