Preheat oven to 325F.

Peel potatoes and cut in half lengthwise.

Cut each half into thin slivers.

Heat olive oil in an oven-safe pan over medium heat.

Add potatoes, onion, garlic, parsley, and thyme to the pan.

Saute the vegetables until potatoes are partially cooked.

In a separate bowl, beat eggs with salt and pepper.

Set the egg mixture aside.

Add sliced tomatoes to the pan with the potatoes and continue to saute until all vegetables are cooked and tender.

Ensure most of the moisture from the tomatoes has evaporated from the pan.

Press the potato mixture down evenly in the pan.

Pour the beaten eggs over the vegetables.

Sprinkle grated cheddar cheese evenly over the eggs.

Place the pan in the preheated oven and bake for about 20 minutes, or until the eggs are set.

Remove from oven and let cool slightly before slicing.

Cut into slices and serve warm, at room temperature, or cold.