Cook fresh peas uncovered in seasoned, rapidly boiling water for 3-5 minutes. Remove from heat. Strain and chill peas rapidly in an ice bath; drain and set aside.
Sauté chopped shallot in olive oil and butter over medium heat until soft. Add Chardonnay to the pan and reduce by one half. Add heavy whipping cream and bring to a simmer. Allow shallot mixture to cool.
Combine peas, cooled shallot mixture and freshly chopped herbs in a food processor and purée. If purée is too thick, adjust to desired consistency by adding a bit of mineral water; chill for approximately one hour.
To serve, toss the crab in hazelnut oil, season with salt and pepper and mound the crab in the center of 6 shallow bowls. Ladle pea soup around the crab and garnish with herbs, blossoms and a drizzle of pistachio oil.