Toast the walnuts. Put the walnuts in a dry skillet over medium heat. Toast for about 5 minutes, shaking the pan often, until they smell nutty and have darkened a shade. Tip them straight out onto a plate — they'll keep cooking and burn in the hot pan. Chop coarsely once cool.
Warm the rosemary into the oil. Combine the olive oil and chopped rosemary in a small saucepan over low heat. Warm for about 2 minutes, just until fragrant — it should barely whisper, never sizzle. Take it off the heat and leave it to steep for 10 minutes. This step is what keeps the dressing from tasting sharp and piney. Don't skip it.
Wash and dry the greens while the oil steeps. Beet greens hold grit, so swish them in a big bowl of water and lift them out rather than pouring the water off. Dry them thoroughly in a salad spinner — wet leaves won't hold dressing.
Prepare the figs. Trim the stems. If your figs are ripe but still firm, slice each one into 4–5 rounds. If they're very ripe and soft, quarter them instead — thin slices will collapse. Leave them at room temperature.
Make the vinaigrette. In a pint jar, combine the balsamic vinegar, honey, mustard, sea salt and pepper. Cover and shake until the salt dissolves. Add the rosemary oil, rosemary leaves and all, cover again and shake hard until it comes together. Taste it — it should be bright but not sharp. If it makes you wince, add another tablespoon of olive oil.
Assemble. Toss the greens with about 2 tablespoons of the vinaigrette, just enough to coat lightly, and divide between four plates. Arrange the figs on top. Scatter over the mizythra and toasted walnuts. Drizzle about a teaspoon more dressing over each plate and finish with flaky salt and freshly ground pepper.
Serve immediately, with the remaining vinaigrette in the jar on the table.