Heat the olive oil in a 30 cm / 12-inch wide skillet or shallow pot over medium heat. Add the chopped onion and cook for 5 to 6 minutes, stirring now and then, until soft and light gold.
Add the garlic and cook for 30 seconds, until fragrant.
Add the green beans and potatoes. Stir to coat everything in the oil and cook for 3 to 4 minutes.
Pour in the crushed tomatoes, tomato paste, and water. Add the sugar, salt, pepper, and oregano, then stir to combine.
Bring the sauce to a gentle simmer, cover the pot, and turn the heat down to low. Cook for 35 to 40 minutes, stirring every 10 minutes or so.
Check the beans at the 35-minute mark. They're ready when they're fully soft, almost falling apart, not crisp-tender like a quick saute.
If the sauce still looks thin, uncover the pot for the last 5 to 10 minutes to let it reduce and thicken.
Taste the sauce and add more salt if needed, since canned tomatoes vary in saltiness.
Stir in the fresh parsley and remove the pot from the heat.
Serve warm or at room temperature, with crusty bread and feta on the side if you like.