Preheat oven to 400 degrees. Prepare the first four ingredients and place on half-sheet sized baking sheet with lip. Throw thyme stems on top. Drizzle with EVOO and Balsamic. Add salt and pepper. Toss slightly. Arrange so vegetables are mostly cut side down. Bake for 45-50 minutes. Remove veg and any juices from baking sheet to dutch oven (or similar) over medium-high heat. Add tomato paste and stir to combine. Add stock. Cover and bring to boil. (About 5 mins.) Reduce heat to low and simmer covered for 20 minutes. Pull thyme stems from mixture. Hit with immersion blender on low, using caution. Several downward passes work best. Blend to desired consitency. Serve with basil chiffonade as garnish, if desired.