Peel and coarsely grate the beetroot, then measure out 1 cup and place it in a mixing bowl.
Coarsely grate the halloumi and add it to the bowl.
Add the lemon zest, grated garlic, and cumin seeds. Season with salt and black pepper.
Pour in the beaten egg and mix well until fully combined. Set aside for a few minutes.
Heat a frying pan over medium heat. When hot, add the olive oil.
Drop spoonfuls of the mixture into the pan, gently flattening them slightly.
Fry for about 3 minutes on each side until golden and cooked through.
Cook in batches if needed — you should end up with around 8–10 fritters.
Remove from the pan and allow to cool slightly before serving.
Serve warm or at room temperature in a bagel or bun with salad leaves and your choice of relish or chutney. They also work well as part of a mezze-style spread or packed lunch.