Position an oven rack about 4-6 inches from the broiler and preheat the broiler on high.
Place the whole tomatoes on a baking sheet and broil, turning them every few minutes with tongs, until the skins are blistered and lightly charred all over. This should take about 10-15 minutes.
Carefully transfer the hot tomatoes to a bowl.
Let them cool just enough to handle, or run them under cold water for a moment. The skins should slip off easily.
Discard the skins.
Cut the peeled tomatoes into large chunks and transfer them to a blender or food processor.
Blend until you have a smooth purée.
In a large, heavy-bottomed skillet or pot, melt the butter over medium heat.
Add the crushed basil, black pepper, saffron threads, and thyme.
Sauté the spices, stirring constantly, for about 2 minutes until fragrant.
Pour the tomato purée into the skillet with the spices.
Stir in 2 teaspoons (10 ml / 0.3 fl oz) of salt.
Bring the mixture to a gentle bubble, then reduce the heat to low.
Simmer the purée very gently, uncovered, for about 1. 5 hours.
Stir occasionally to prevent it from sticking. The purée will reduce and thicken considerably.
Once the purée is very thick, stir in the heavy cream. Increase the heat to medium-high and stir continuously just until the sauce returns to a thick, paste-like consistency. Be careful not to let it boil rapidly.
Taste and adjust seasoning if needed.
Serve warm as a rich, cooling accompaniment to spicy dishes.