Peel and chop the onion then fry it gently in a pan with a little olive oil.
Drain and rinse the cannellini beans, add them to the pan and go on frying for a few minutes.
Remove the beans from the heat, chop the olives and add them to the beans, season with some pepper.
Blend the cannellini and olives to get a smooth sauce then set aside.
Wash the tomatoes, cut them into half and cook them in a pan with a little olive oil, for 5 minutes. Season with salt and chopped fresh basil.
Prepare a large pot filled with water and add a handful of coarse salt. Bring to a boil.
Cook the lasagne sheets into the boiling water, two or three sheets at a time, for a couple of minutes. As you drain the sheets, place them in a large bowl filled with cold water, let them cool a few minutes then lay them on a clean kitchen towel.
Preheat the oven to 400°F and line a baking pan with wet parchment paper.
Add a small ladle or two of pasta cooking water to the cannellini bean sauce and mix well, until smooth.
Start to compose the lasagna with a first layer of pasta, then one of cannellini sauce then top with some cooked tomatoes.
Continue alternating layers of lasagne sheets and filling until you finish the ingredients. Keep in mind that the last layer must be made of cannellini sauce and tomatoes.
Pour into the lasagna pan a small ladle of pasta cooking water, cover with aluminum foil and bake for 20 minutes.
Remove now the aluminium foil, turn on the grill and bake for ten minutes more, until the lasagna surface gets golden.
Remove from the oven and serve immediately.