In a skillet, melt the butter and sauté the carrots and asparagus pieces until they are just tender and browned. Remove them from the skillet and place them in a medium-sized mixing bowl, and set aside.
In the same skillet, add the chopped walnuts and toast over medium heat just until fragrant. Remove from the skillet and set aside. These will be used for the topping.
In a small bowl, combine the yogurt, grated cucumber, lemon juice, garlic, dill, and honey (optional, to add a hint of sweetness), and season with Kosher salt.
Spread the Tzatziki dressing on the bottom of a small plate.
In the mixing bowl with the sautéed carrots and asparagus, add the quartered beets. Season with Kosher salt, and drizzle about a tablespoon of olive oil over the carrots and beets, then gently toss.
Add the seasoned mixed vegetables on top of the Tzatziki base and top with crumbled feta and toasted walnuts.
Serve immediately.