Place the eggplant and zucchini pieces in a colander and sprinkle them generously with kosher salt. Let them sit for 30 minutes to draw out excess moisture. Rinse the vegetables and pat them dry.

In a large, heavy-bottomed pot or Dutch oven, heat 1 tablespoon of oil over low to medium heat. Add the chopped onion and sauté until translucent, about 5-7 minutes. Add the minced garlic and cook for an additional 2 minutes until fragrant. Set aside.

Heat another tablespoon of oil in the same pot. Add the cubed potatoes and cook, stirring occasionally, until they start to brown and soften, around 10 minutes. Remove and set aside.

In the same pot, add more oil as needed, then add the eggplant. Sauté until it starts to brown and becomes tender, about 8-10 minutes. Remove the eggplant from the pot.

Add additional oil if required, then toss in the zucchini and sauté until slightly browned and tender, approximately 5-7 minutes. Set aside.

Repeat the process with the bell peppers, stirring until they soften and brown slightly, about 5-7 minutes. Remove from the pot.

Return the sautéed onion, garlic, potatoes, eggplant, zucchini, and bell peppers to the pot. Add the crushed tomatoes, vegetable broth, and halved cherry or grape tomatoes.

Cook uncovered over medium-low heat, stirring occasionally, until the vegetables are tender and the flavors meld together, about 30-40 minutes. If the stew appears too watery, increase the heat slightly and cook for a few more minutes, stirring frequently.

Just before serving, stir in the chopped basil and parsley. Taste and adjust seasoning as needed.

Garnish with extra basil and parsley, and sprinkle with grated Parmesan or vegan Parmesan.