Preheat a large pot over medium heat. Add 2 tablespoons of olive oil and heat until shimmering. Add the carrot, celery and onion, season with a pinch of salt and cook, stirring, until the vegetables are softened, around 10 minutes. Add the ground beef and cook, crumbling it into small pieces with a spatula, until browned, around 8 minutes. Add the garlic, tomato paste and thyme and cook, stirring, until the tomato paste is incorporated, around 2 minutes. Add the tomato passata, basil, and black pepper, bring the sauce to a simmer, lower the heat to low and cook, stirring occasionally, until the beef is tender, around 1 hour. Taste the sauce for seasoning and adjust with salt and pepper, as desired.

Remove the pot from the heat and set aside at room temperature to slightly cool. Leftovers can be refrigerated for up to 5 days or frozen for up to 6 months.

Line a large sheet pan or tray with paper towel. Arrange the eggplant slices in a single layer and lightly season both sides with salt. Cover with a sheet of paper towel and repeat the process with the remaining eggplant slices. Repeat the process with the zucchini slices. Set aside for 15 to 20 minutes to allow for excess moisture to drain from the vegetables.

Preheat your Traeger grill to 500F or a grill pan over medium-high heat. Lightly brush the eggplant and zucchini with olive oil and cook in batches until grill marks form, around 3 minutes. Flip and cook the other sides until grill marks form and the vegetables are slightly softened but not fully cooked through, around 3 more minutes. Transfer the zucchini and eggplant to individual platters and set aside.

Evenly spread a thin layer of meat sauce on the bottom of a deep roasting tray. Top with a single layer of eggplant, followed by a layer of meat sauce and a layer of shredded mozzarella cheese. Repeat the process, alternating between the zucchini and eggplant slices until the roasting tray is full. Finish with an even layer of grated Parmigiano Reggiano.

Lower the heat on the Traeger to 425F or preheat your oven to 400F. Cover the lasagna with a sheet of parchment paper and seal the top tightly with a layer of foil. Bake on the Traeger Grill or in your oven for 30 minutes or until the sauce is bubbling and the cheese has melted. Remove the foil and parchment paper and continue baking until the top layer of cheese is golden brown and the edges are crispy, around 15 to 20 minutes.

Remove the lasagna from the oven and let it rest at least 20 minutes before slicing and serving.