In a small saucepot over medium heat, add all ingredients for the infused oil. Once the oil begins to lightly bubble, remove from the heat and let the oil infuse and cool down, about 30-60 minutes.

Once cool, store in an airtight container.

Place the bell pepper over direct flame and cook until the surface is fully charred. Transfer the pepper to a large bowl and cover with plastic wrap. Leave the pepper to steam for a few minutes, then using a clean kitchen towel and gloves, peel the charred skin from the bell pepper. De-stem and de-seed the pepper. Set aside.

In a medium saucepan over medium-low heat, add the infused olive oil, shallot, and garlic with a generous pinch of salt. Stir and cook until the aromatics are translucent, about five minutes.

Transfer the shallots and garlic to a high-powered blender, along with the reserved bell pepper and tomato sauce. Blend on high until the sauce is completely smooth.

Pour the sauce into a 12-inch (30-centimeter) skillet or copper pan. Season with salt, as well as sugar, if needed. Cook over medium-low heat until the sauce reduces slightly.

Reserve ¼ of the piperade for the piperade vinaigrette.

Preheat the oven to 300°F (148°F). Cut a piece of parchment to fit directly over the cooking pan.

Arrange the zucchini, squash, eggplant, and tomato in alternating order in the casserole pan, from the edge to the center. Keep them tightly shingled, about ⅛ to ⅙ inch (three millimeters) apart.

Once the pan is filled, lightly drizzle the infused olive oil onto the shingled vegetables, followed by black pepper and salt, and a sprig of thyme.

Cover the casserole pan with the prepared parchment and bake for 30 minutes for tender, crisp vegetables, or two hours for a more stewy, traditional confit byaldi.

Add reserved piperade sauce, Dijon mustard, vinegar, salt, and pepper to a small bowl. Whisk to combine.

While whisking, slowly drizzle in three tablespoons of infused olive oil. Whisk until emulsified.

Taste and season with salt and pepper. Set aside.

Mound the confit byaldi in the center of a plate. Drizzle the plate with some piperade sauce and piperade vinaigrette. Top dish with chives and parsley. Serve with a toasted baguette.