To make the starter, combine the yeast, sugar, rye flour and 435ml (15¼fl oz/1¾cups) warm water in a bowl. Cover with plastic wrap and set aside overnight at room temperature to sour. For a stronger flavour, leave for up to 3 days.
Brush a large baking tray with oil or melted butter. To make the bread dough, combine the rye flour, 440g (15½oz/3½cups) of the plain flour, sugar, caraway seeds and 2teaspoons salt in a large bowl. Dissolve the yeast in 250ml (9fl oz/1cup) warm water. Make a well in the centre of the dry ingredients and add the sourdough starter, dissolved yeast and oil. Mix, using a wooden spoon then your hands, until the dough forms a rough, slightly sticky ball, which leaves the side of the bowl. Add some of the remaining flour, if necessary — you may not need to use it all.
Turn onto a lightly floured work surface. Knead for 10 minutes, or until smooth and elastic. Incorporate the remaining flour, if needed. Place the dough in a large, lightly oiled bowl. Cover with plastic wrap or a damp tea towel and leave in a draught-free place for 45 minutes, or until well risen. Punch down and knead for 1 minute.
Divide the dough into two even-sized portions. Shape into round or oblong loaves and place on the baking tray. Sprinkle with rye flour and use the end of a wooden spoon handle to press holes 2cm (¾inch) deep in the top, or make three slashes. Cover the dough and leave in a draught-free place for 45 minutes, or until the dough is well risen.
Preheat the oven to 180°C (350°F/Gas 4). Sprinkle the loaves with a little extra flour. Bake for 40 minutes, or until golden and the bread sounds hollow when tapped on the base. Cool on a wire rack.