Bring tomato juice, ½ cup water, oil, salt, rosemary and garlic to a simmer in a small saucepan. Transfer to a medium bowl. Cool until lukewarm.
Sprinkle yeast over lukewarm water in a small bowl. Leave until foamy, 5 minutes. Stir to dissolve.
Add yeast mixture to tomato juice mixture. Gradually stir in rye flour. Gradually knead in plain flour until dough comes together and is workable (dough will be sticky). Knead in the sun-dried tomatoes. Turn dough out onto a floured work surface. Knead for 1 minute. Let rest for 10 minutes.
Knead dough again on lightly floured surface until smooth and elastic, about 10 minutes; add more plain flour as needed if dough is very sticky (dough should be slightly sticky). Place dough in a lightly oiled bowl. Turn to coat. Cover loosely with plastic wrap. Leave to rise in a warm place until doubled in volume, about 1 hour.
Punch dough down. Lightly coat a 23 x 13 cm loaf pan with olive oil. Place dough in pan, patting it into the corners. Cover loosely with plastic wrap. Leave to rise in a warm place until doubled in volume (risen above top of pan), about 1 hour.
Preheat oven to 190°C. Bake until the loaf sounds hollow when tapped on the bottom, 40 to 50 minutes. Turn out onto a wire rack. Cool completely before slicing.