Cook linguine in a large saucepan of boiling, salted water according to packet directions. After 5 minutes of cooking, add broccolini. When pasta is cooked and broccolini is tender, drain, reserving ¼ cup of cooking liquid.
Meanwhile, heat olive oil in a small frying pan on medium. Cook garlic and chilli until garlic begins to colour, without becoming too browned.
Return linguini, broccolini and reserved cooking liquid to saucepan. Stir in garlic and chilli mixture and toss on medium heat. Season to taste. Add ricotta in spoonfuls and mix together very lightly. Serve in heated serving bowls.