Snap woody ends off asparagus stalks and discard. Cut asparagus into 3cm pieces. Wash well, drain, and set aside.
Slice chicken breasts very thinly and place in bowl. Season with salt, pepper, oregano, and a drizzle of olive oil. Set aside.
Heat the oil in a heavy, wide pan on medium heat. Add shallots and cook gently for 5 mins or until soft, not browned, stirring often. Add rice and stir continuously for a few minutes until it turns glossy and cream-coloured. This step is very important.
Stir in wine, if using. Reduce heat slightly to simmer gently. Once evaporated, add stock, one to two ladlefuls at a time, stirring between each addition. The stock will absorb within 5 to 7 minutes. Continue this cycle of adding stock, stirring, simmering for about 3 to 4 cycles.
As rice is cooking, cook the chicken. In a medium-sized pan, heat oil. Add chicken and saute until cooked and golden. Remove from pan and set aside.
In the same pan as chicken, add asparagus with a ladle of stock. Place lid on pan and let cook for about 2 minutes.
Taste the rice for doneness. It should be creamy with a slight bite.
Add the chicken, asparagus (and stock that it cooked in), butter, parsley, and grated cheese. Stir to incorporate well. Add one last ladle to moisten if rice looks dry. Taste for seasonings. Drizzle with a little olive oil. Serve immediately.