Cook fettuccine and reserve 2/3 of pasta water.
In a small bowl combine egg yolks and parmesean. Set aside.
In a large pan over medium heat, saute chanterelles and garlic in 1 tbsp butter and 1 tbsp olive oil for about 3 minutes.
Add remaining 2 tbsp butter and baby kale, saute for 1 minute.
Remove from heat and add fettuccine, egg yolk mixture and reserved pasta water. Toss together to coat. Serve immediately with burrata and chive pistou drizzled over the top.