Preheat oven to 375 degrees F. Remove the stems from the mushrooms and chop the stems finely.
In a nonstick frying pan over medium-high heat, bring the chicken broth to a boil. Add the shallot and mushrooms stems; cook, stirring occasionally, until the vegetables are tender and most of the liquid has evaporated, about 2 minutes.
In a medium-size bowl, combine the vegetable mixture, rice, mayonnaise, tarragon, and half the parmesan cheese; set aside.
Using a paper towel, wipe out the frying pan and place over medium heat. Add the olive oil and mushroom caps; sauté until coated with oil, 20 to 30 seconds.
Remove from pan and arrange the mushroom caps, stem end up, on a baking sheet. Mound about 2 teaspoons of the prepared vegetable/rice mixture in each mushroom cap. Sprinkle with the remaining Parmesan cheese. NOTE: If made in advance, cover with plastic wrap and refrigerate for up to 8 hours.
Bake until the cheese is lightly browned and the mushrooms are tender but still hold their shape, about 10 minutes. To serve, dust each cap lightly with paprika.
Makes 6 servings (3 each stuffed mushroom caps).
Tarragon-Rice Stuffed Mushrooms Recipe: https://whatscookingamerica.net/tarragonmushroom.htm