Preheat oven to 350°.
Line a large sheet pan with parchment paper. Cut tomatoes in half and remove any core and green parts. Spread face up on the baking sheet. Drizzle with olive oil and season with salt and pepper. Roast for 15 - 25 minutes, depending on water content of tomatoes, until soft.
While tomatoes are roasting, chop eggplant, onion, peppers, and mushrooms into similar sized small chunks. Add to baking sheet and return to oven for about 20 minutes, stirring after 10.
Mince garlic and add to vegetables, roast for another 10 minutes or until most of the liquid is reduced and veggies are very soft.
Carefully pour contents of sheet pan into large pot. Add olives, vinegar, sugar, tomato paste, basil and oregano. Stir to combine and bring to a simmer for about 15 minutes. Taste and adjust seasoning if necessary.
Ladle antipasto into clean jars. Refrigerate over night before serving.
Can be processed for longer storage. Using safe food canning method, use clean sterilized jars and new lids and process jars according to size, between 8 and 15 minutes.