Preheat oven to 400°F and line 11-inch tart pan with parchment paper.
Make the tart
Rinse millet and drain. In Dutch oven over medium heat, toast millet, stirring continuously, until dry and fragrant (about 5 minutes). Pour in stock and stir in carrot, parsley, lemon zest, and salt. Reduce heat and simmer covered until liquid is absorbed (about 25 minutes). Remove from heat and mash with wooden spoon, adding water 1 tablespoon at a time if needed to make millet soft and mushy. Scoop into lined tart pan. Cover with second piece parchment paper and press to form even base with raised edge. Remove the top piece of parchment paper and set tart aside.
Make the filling
Place garlic cut-side up on sheet of foil. Rub with olive oil, wrap foil around bulb, and place in oven. Halve small tomatoes and cut larger tomatoes into 1/2-inch slices. Rub both sides with olive oil and spread in single layer on baking sheet. Place in oven and roast 1 hour (or until starting to shrivel). Place millet tart in oven and roast for the final 20 minutes. Remove everything from oven and cool slightly.
Remove tart from pan, peel and discard parchment paper, and transfer tart to serving dish. Squeeze root end of roasted garlic to release cloves and spread onto tart. Brush with olive oil and cover bottom of tart with large slices of tomatoes. Top with smaller tomatoes, sprinkle with salt, pepper, and thyme. Drizzle with vinegar and serve.