Position 1 oven rack in the top third of the oven and 1 rack in the bottom third. Preheat to 375 degrees. Spray 2 large rimmed baking sheets with nonstick cooking spray.
Melt the butter with olive oil in a small saucepan over medium-low heat.
Combine the red beets, a large pinch of thyme, large pinch of savory and 1 Tbsp of the melted butter mixture in a medium bowl. Sprinkle with salt and pepper and toss to coat.
Turn the beets onto 1 side of 1 prepared sheet.
Combine all the remaining vegetables and herbs, garlic, shallots and remaining butter mixture in a large bowl. Sprinkle generously with salt and pepper and toss to coat.
Divide the vegetable mixture between prepared baking sheets.
Roast the vegetables for 30 minutes. Reverse the baking sheets and continue to roast until all the vegetables are tender. (about 45 minutes or longer)
This dish can be prepared 4 hours ahead. Let it stand at room temperature. Rewarm in a 350-degree oven about 20 minutes. Transfer to a platter to serve.