1. Preheat oven to 400°F. Spread vegetables in a single layer on a parchment-lined baking sheet. (Spread beet on a separate lined sheet so it doesn't stain the other vegetables.) Toss with oil; season with salt and pepper. Roast vegetables, stirring halfway through, until tender and evenly browned, about 30 minutes.
2. Arrange phyllo shells in a single layer on a baking sheet. Bake for 2 to 3 minutes to crisp. Set aside to cool.
3. Blend cheeses, zest, thyme and 1/4 tsp. each salt and pepper in a food processor until smooth. Transfer mixture to a ziplock bag. Snip a small hole in one corner; pipe into each shell. Place roasted vegetables on top. Garnish with fresh thyme. Serve warm or at room temperature.