Preheat oven to 300 degrees F (150 degrees C).

Arrange tomatoes, cut-side up, on a baking sheet. Whisk 1/4 cup olive oil, garlic, oregano, salt, and pepper together in a bowl; spoon over tomatoes.

Bake tomatoes in the preheated oven until slightly shrunken, 3 to 4 hours.

In the last hour of the tomatoes baking, thinly slice eggplant and sprinkle with salt; set aside until some of the water starts to bead on the slices, about 30 minutes. Rinse the salt off the eggplant and transfer to a bowl. Pour remaining 1/4 cup olive oil and sprinkle paprika over eggplant slices; toss with your hands to coat.

Arrange eggplant slices in a single layer in a skillet over medium heat; cook until tender, 3 to 4 minutes.

Alternate tomato slices and eggplant slices on serving plates creating 'towers.' Drizzle yogurt and honey over each 'tower'; top with almonds.