Prepare the ingredients: peel and finely chop the onion and garlic. Roughly chop the fresh dill.
In a medium saucepan, heat the olive oil over medium heat. Add the chopped onion and sauté for 3-4 minutes, until translucent.
Add the chopped garlic and cook for another minute, until fragrant.
Pour in the tomato puree, then add the salt, pepper, and sugar. Stir well to combine, then bring to a simmer.
Once simmering, reduce the heat to low and cook for 10 minutes to allow the flavors to meld.
Add the heavy cream and stir thoroughly to create a creamy consistency. Cook for an additional 5 minutes over low heat.
Finally, stir in the fresh dill and cook for 2 minutes more. Taste and adjust the seasonings as needed.
Let the sauce cool slightly, then serve with pasta, meat dishes, or grilled vegetables.
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