For the marinated veggies: Mix the oil, vinegar, thyme, Dijon, honey and garlic together. Season with salt and pepper and set aside.
Clean the gills of the portobello mushrooms by using a spoon and scraping out the black gills from the underside of the cap.
Place all the vegetables in a baking dish and then pour the marinade over them and toss. Allow the marinade to work its magic for 15 to 30 minutes.
Heat a grill pan over medium-high heat.
Grill the vegetables, in batches if necessary, until nice grill marks appear, 3 to 5 minutes a side. Set the cooked vegetables aside until ready to assemble (you can place them back in the baking dish where they were marinating). Once the mushrooms come off the grill, slice them thinly on the diagonal.
For the spread: Mix the goat cheese with the sun-dried tomatoes and season with some salt and pepper.
For the naan-wich build: Lightly brush the naan with oil and grill on both sides, just until some grill marks appear, 2 to 3 minutes per side. Start by schmearing some of the goat cheese spread on each piece of the griddled naan, and then layer the grilled vegetables high and top with a generous amount of basil, closing the naan-wich with the other slice of naan. Slice the sandwich on the diagonal and then enjoy feeling healthier with each bite.