Preheat oven to 375°F. Whisk oil, vinegar, and garlic in small bowl to blend. Season dressing generously with salt and pepper

Cut green tops off beets; reserve tops. Arrange beets in single layer in 13x9x2-inch baking dish; add 1 cup water. Cover; bake until beets are tender when pierced with knife, about 1 hour 10 minutes. Peel beets while warm. Cut beets in half and slice thinly. Transfer to large bowl. Mix in capers and 1/4 cup dressing. Season with salt and pepper

Cut stems off beet greens; discard stems. Wash greens. Transfer greens, with some water still clinging to leaves, to large pot. Stir over high heat until just wilted but still bright green, about 4 minutes. Drain greens; squeeze out excess moisture. Cool; chop coarsely.

Transfer greens to medium bowl. Toss with enough dressing to coat. Season to taste with salt and pepper

Arrange beets in center of platter. Surround with greens; sprinkle with feta. Drizzle with any remaining dressing.