Preheat oven to 400°F (200°C). Wrap each beet individually in aluminum foil. Place on a baking sheet and roast for 40–50 minutes, until fork-tender. Let cool completely, then peel off skins (they should slip off easily). Cut beets into wedges.
While beets roast, place cucumber slices in a colander and sprinkle with 1/2 teaspoon salt. Toss to coat and let sit for 10 minutes to draw out excess moisture. Pat dry with paper towels.
In a small bowl, whisk together olive oil, lemon juice, Dijon mustard, minced garlic, and a pinch of salt and pepper until emulsified.
In a large bowl, combine beet wedges and cucumber slices. Pour dressing over and toss gently to coat.
Transfer salad to a serving platter. Scatter crumbled goat cheese on top. Garnish with fresh dill or mint if using. Serve immediately or refrigerate for up to 2 hours before serving.