Sift the flour and salt into a large bowl and add the sugar and yeast. Stir in the measured warm water and 3 tablespoons of the oil. Mix well to form a smooth dough, then turn out on to a well-floured surface and knead for 10 minutes until smooth and elastic. Cover and allow to rest for 15 minutes before kneading again for a further 10 minutes. Return to the bowl, cover with clingfilm and allow to stand for 30 minutes.
Knead the dough again to knock out the air, then cut into 4 pieces. Cut each quarter into 4 pieces, then stretch and roll each piece to make a long breadstick shape. Brush a baking sheet with the remaining oil. Roll the breadsticks in the oil, then sprinkle half with the sesame seeds and half with the poppy seeds. Bake in a preheated oven, 180°C (350°F), Gas Mark 4, for 30 minutes until golden and crisp. Remove from the oven and allow to cool.
Meanwhile, place the peppers on a baking sheet with the tomatoes and drizzle with the oil. Roast for 30 minutes in the oven with the breadsticks. Remove and place in a polythene bag and allow to cool. Remove from the bag and peel away the skins and discard. Place in a food processor with all the cooking juices, vinegar, cheese and thyme, if using and whiz until well blended and rough-textured. Transfer to a serving bowl and serve with the breadsticks.