Mix the flour, herbs, salt and yeast in a bowl. Add the water and oil, mix. Knead to form a soft, smooth dough, cover and leave to rise for approx. 2 hrs. at room temperature.
Divide the dough into eighths. On a lightly floured surface, flatten, stretch or roll out the pieces of dough (each approx. 13 cm in diameter). Spread 1 tbsp of tomato puree on each piece, leaving a border of approx. 1 cm.
Top one half of each piece of dough with the tomatoes, salami, mozzarella and basil, season. Fold the free half over the filling. Press the edges down firmly. Dust the panzerotti with a little flour.
Fill a pot to 1/3 with oil and heat it to approx. 160 °C (see tip). Using a slotted spoon, lower the panzerotti into the hot oil in batches. Deep-fry for approx. 3 mins., turn and fry for a further 3 mins. until cooked. Remove and drain on paper towels.