Preheat the oven to 400 degrees Fahrenheit.
Spread the pistachios in a pie tin and toast in the oven for 6 to 8 minutes, or until golden brown, stirring once or twice. Pour immediately onto a plate to cool. Chop coarsely and set aside.
To make compote, in a large saucepan over medium-high heat, stir together the clementine zest and juice, sugar, and water, and bring to a boil, stirring to dissolve the sugar. Reduce the heat to medium-low and let the mixture summer until slightly thickened, about 3 minutes. Add the rhubarb, return to a simmer, and cook until rhubarb in tender when pierced with a fork, about 20 minutes. Add the strawberries, reduce to low, and continue to simmer until the fruit is broken down and the juices have thickened, about 40 minutes longer, stirring occasionally to make sure the bottom doesn’t scorch. The consistency of the compote should be a little looser than jam. Remove from the heat and cover to keep warm. (If preparing ahead of time, let cool, cover tightly, and refrigerate for up to 5 days. Bring to room temperature or reheat gently before serving).
To make the honeyed yogurt, in a bowl, whisk together the yogurt and honey. Using the tip of a small, sharp knife, scrape the seeds from the vanilla bean into the yogurt mixture and stir to mix well. Discard the bean pod (or reserve for another use).
To serve, divide the yogurt among 4 bowls. Scoop the compote over the top of each portion, dividing it evenly, and sprinkle generously with toasted pistachios. Serve immediately.