Warm the vegetable broth in a small pot over low heat, or in the microwave, and keep it near the stove.
Heat the olive oil and butter in a 30 cm / 12-inch skillet over medium heat until the butter melts.
Add the onion and cook for 3 to 4 minutes, stirring often, until soft and see-through.
Add the garlic and cook for 30 seconds, until fragrant.
Add the orzo and stir for 1 to 2 minutes, until the grains look lightly toasted and are coated in the oil.
Add the warm broth one ladle (about 120 ml) at a time, stirring often and waiting until most of the liquid is absorbed before adding the next ladle. This takes about 12 to 15 minutes total.
Once the orzo is tender but still has a slight bite and the mixture looks creamy, stir in the spinach in handfuls, letting each batch wilt before adding more, about 2 minutes.
Remove the skillet from the heat. Stir in the lemon zest, lemon juice, and feta until the feta softens into the orzo and the sauce looks creamy.
Season with black pepper and salt, taste, and adjust as needed since feta and broth are both salty.
Spoon into bowls, top with extra feta and chopped dill, and serve right away.