Place the bread flour in a large bowl (or the bowl of a stand mixer fitted with a dough hook), add the yeast to one side and the salt and sugar to the other. Stir to combine.
Pour in the olive oil and water and mix to form a rough dough.
Knead, either by hand on an unfloured surface or with the stand mixer on a medium/high speed, for 5-10 minutes until the dough is smooth and elastic. It should be slightly tacky to the touch but should pull away from the sides of the bowl cleanly. If it feels wet then you can add a little more flour but be careful, the dough is meant to be a bit sticky.
Thoroughly dry the sun dried tomatoes with kitchen paper then chop them into small pieces. Finely chop the basil.
Add the tomatoes and basil to the dough and knead through until they are evenly distributed. Add a little extra flour if needed to counter the extra moisture.
Place the dough in an oiled bowl, cover and set aside to rise until doubled in size, about 1-2 hours.
Punch down the risen dough and give it a brief knead to knock out any air bubbles. Divide the dough into 14 pieces. I use a scale for accuracy.
Line two baking sheets with baking parchment and sprinkle them with fine semolina or cornmeal (optional).
Roll each piece of dough out using your hands into a long, thin rope. Place them spaced apart on the baking sheets.
Loosely cover with oiled clingfilm or baking parchment and set aside to rise for about 30 minutes until they are puffy and spring back slowly most of the way if you poke one gently with a finger.
Meanwhile, preheat the oven to 220°C/200°C fan/425°F/gas mark 7.
Gently brush the risen breadsticks with olive oil. Bake for 12-15 minutes until nicely browned. Transfer the baked breadsticks to a wire rack to cool slightly before serving.