I usually don't have a problem with them getting woody. I'd let them go a while.
I've done something similar to this recipe with red beets. Delicious. I know this is not beet greens, but I think it is worth sharing.
2 bunches golden beets, about 6 to 8 beets
4 tablespoons brown sugar, packed
3 tablespoons apple juice or orange juice
1 tablespoon butter
1/4 teaspoon salt
1/8 teaaspoon freshly ground black pepper
Preparation:
Cut leaves and stems from the beets and scrub; put the whole, unpeeled beets in a large saucepan and cover with water. Bring to a boil; cover and simmer over medium heat for 20 to 30 minutes, until tender.
Slip skins from beets and cut into 1/4- to 1/2-inch pieces.
In a large skillet or saute pan, combine the brown sugar, juice, and butter. Bring to a simmer over medium heat. Add the beets and cook, uncovered, stirring frequently, until the liquid has evaporated and beets are glazed, about 5 to 7 minutes.
Now for the greens.
I have used a variation of the below for beet greens, chard, and kale. I got the original recipe from Hattie, but copying it is less typing. I usually brown some onions before I add the greens. Don't worry about the garlic clumping together. When you add the greens and stir them up, the garlic will get distributed. I also like to add paprika while browning the onions. This is just a basic recipe. Have fun with it.
Ingredients
2 bunches beet greens, stems removed
1 tablespoon extra-virgin olive oil, or to taste
2 cloves garlic, minced
1/4 teaspoon crushed red pepper flakes (optional)
salt to taste
freshly ground black pepper to taste
2 lemons, quartered
Directions
1.Bring a large pot of lightly salted water to a boil. Add the beet greens, and cook uncovered until tender, about 2 minutes. Drain in a colander, then immediately immerse in ice water for several minutes until cold to stop the cooking process. Once the greens are cold, drain well, and coarsely chop.
2.Heat the olive oil in a large skillet over medium heat. Stir in the garlic and red pepper flakes; cook and stir until fragrant, about 1 minute. Stir in the greens until oil and garlic is evenly distributed. Season with salt and pepper. Cook just until greens are hot; serve with lemon wedges.