Chop the asparagus stalks finely, leaving the tips whole. Cook the asparagus tips and stalks in a saucepan of simmering water for about 3 minutes until al dente. Drain, reserving the cooking water.
Pour the reserved cooking water over the stock cube in a measuring jug, make up to 900 ml (1½ pints) with boiling water and stir to dissolve the cube.
Meanwhile, melt the butter with the oil in a saucepan, add the onion and cook over a medium heat for about 2 minutes, until softened. Stir in the rice and cook for 1 minute, stirring, until well coated in the onion mixture.
Pour in the wine and cook for 2–3 minutes until absorbed. Gradually add the hot stock, 125 ml (4 fl oz) at a time, stirring constantly and cooking until most of the liquid has been absorbed before adding the next batch of stock. Continue until almost all of the stock has been absorbed and the rice is creamy but still firm. This will take about 15 minutes.
Stir in the asparagus tips and stalks and cook for 2–3 minutes until heated through. Stir in the lemon rind and juice, mint and cheese. Cover and leave to stand for about 1 minute. Serve in bowls with extra grated cheese for sprinkling.