1 lb. Pappardelle's Lavender Fettuccine
4 (3 oz.) halibut filets
4 Tbsp. butter, divided
4 Tbsp. neutral oil
2 sprigs tarragon
1 tsp. dried lavender buds
1 tsp. salt
¼ tsp. white pepper
2 Tbsp. sugar
Zest of 2 lemons
2 Tbsp. lemon juice
½ cup heavy cream