Pierce the cherry tomatoes and blanch them in boiling water, cool with ice, discard peel and seeds, put on a baking tray lined with baking paper, season with oil and sprinkle some salt and sugar. Bake at 120°C for 35 minutes.
In a pan heat the oil and golden the shallot slices, pour the frozen asparagus to soften them. Cut the asparagus into pieces without thawing, but leave the tips as they are for a better display.
Drain the spaghetti very firm, pour in a sauté pan with small asparagus, add some pasta cooking water. Mix well, add the caramelized cherry tomatoes, sauté well and serve with fresh basil.
Add a few pecorino sardo flakes to complete the dish.