Preheat oven to 400°F. Place beets on a large sheet of foil, drizzle with 1 tablespoon olive oil, sprinkle with salt, and wrap tightly into a packet. Roast on a rimmed baking sheet until a paring knife slides in easily, 45 to 55 minutes depending on size. Let cool completely, then slip off skins with your fingers and cut into 1-inch wedges. (Can be done 2 days ahead; refrigerate in an airtight container.)

In a small food processor or blender, combine parsley, mint, garlic, lemon juice, vinegar, olive oil, honey, salt, and pepper. Blend until smooth and emulsified, about 30 seconds, scraping down sides as needed. Taste and adjust seasoning - it should be bright and punchy. (Can be made 1 day ahead; cover and refrigerate. Bring to room temperature and shake or whisk before using.)

In a large serving bowl, combine cucumber, rinsed red onion, and chopped dill. Add roasted beet wedges, being gentle to avoid staining everything deep pink (or embrace it - the magenta streaks are part of the charm).

Drizzle with about two-thirds of the herb dressing and toss gently to coat. Scatter walnuts and feta over top, then drizzle with remaining dressing. Finish with extra dill and serve immediately, or let sit for 10 minutes to allow flavors to meld.