Pasta with goats cheese, chicken, asparagus and mushrooms

Ingredients

• 500g pasta, any shape
• 2 tbsp olive oil, divided
• 2 boneless skinless chicken breasts
• salt and freshly-ground black pepper
• 1 brown onion, peeled and minced
• 6 cloves garlic, peeled and minced
• 1 bunch local asparagus, cut into bite-sized pieces, ends trimmed off
• 450g fresh button mushrooms, halved (optional)
• 225g natural ash or chevre goats cheese
• 1/3 cup full cream Gippy milk
• 1/2 cup freshly-grated Parmesan cheese, divided