Preheat oven to 400°F (200°C). Wrap beets individually in foil and roast for 45-60 minutes until tender when pierced with a knife.
Remove beets from foil, let cool, then peel off skins. Set aside.
Heat butter and olive oil in a large skillet over medium heat. Add shallots and garlic, sauté until soft and fragrant, about 3-4 minutes.
Add thyme and rosemary, cook for 1 minute until aromatic.
Add sliced mushrooms and cook, stirring frequently, until all moisture has evaporated and mixture is dry, about 12-15 minutes.
Remove from heat, stir in ricotta, and season with salt and pepper. Let cool completely.
Roll out puff pastry sheets on a floured surface. Sprinkle breadcrumbs down the center of each sheet.
Divide mushroom mixture between pastry sheets, spreading over breadcrumbs. Place one beet in the center of each.
Wrap pastry around each beet, sealing edges with water and pressing firmly. Place seam-side down on a parchment-lined baking sheet.
Brush tops and sides with whisked egg wash.
Bake for 30-40 minutes until pastry is golden brown and crispy.
Meanwhile, reduce balsamic vinegar in a small saucepan over medium heat until it forms a thick glaze.
Let Wellingtons rest for 10 minutes before slicing and serving with balsamic glaze.