How to Make It
In a large saucepan of salted boiling water, cook the parsnips until tender, 8 to 10 minutes. Drain well and transfer to a food processor. Add the butter and half-and-half and puree until smooth. Scrape the puree into a medium saucepan and cook over moderately low heat, stirring frequently, until thick, 15 minutes. Season with salt and pepper. Transfer to a medium bowl and press a sheet of plastic wrap directly on the butter. Let cool completely, then refrigerate until chilled, 30 minutes.
In a mini food processor, combine the basil, parsley and garlic and pulse until finely chopped. With the machine on, stream in the olive oil until smooth. Season the basil oil with salt and pepper.
Preheat the oven to 400°. Arrange the baguette slices on a baking sheet and brush both sides with olive oil. Toast for 8 to 10 minutes, until golden; let cool.
Spread the toasts with the parsnip butter and arrange on a platter. Top with the anchovies, drizzle with the basil oil and serve.