Combine the rhubarb, sugar, orange juice, honey, all the cardamom, and salt in a heavy-bottomed stainless steel 3-qt. saucepan. With a paring knife, slit open the vanilla bean lengthwise, scrape out the seeds with the back of the knife, and add the seeds and the scraped pod to the saucepan.
Bring to a simmer over medium-low heat, stirring often. Simmer until the rhubarb releases its juice and becomes tender but still retains its shape, 5 to 6 minutes. Add the strawberries and simmer until they start to soften and the rhubarb breaks down slightly, 1 to 3 minutes.
Pour the mixture into a bowl. Make an ice bath by filling a larger bowl with ice and water. Chill the compote over the ice bath at room temperature, stirring occasionally, until completely cool, 10 to 15 minutes. Discard the vanilla pod. Taste the compote and add more sugar and orange juice, if needed.