Preheat the broiler. Combine water and gelatin in a small saucepan and set aside to let soak. Meanwhile, spread the marshmallows over an oiled foil-lined baking sheet and broil until golden brown on top, up to 3 min. Be careful of scorching. Set aside.
Using a stand or hand mixer, blend together the cream cheese, sugar and vanilla until light and smooth, scraping the sides of the bowl with a rubber spatula as needed. Blend in the yogourt. Set aside.
Bring the saucepan of soaked gelatin to low heat, stirring until the gelatin is dissolved. Mix the gelatin mixture into the cream cheese mixture. Fold in the toasted marshmallows and 2/3 of the brownie pieces. Pour into the pie crust and spread evenly. Garnish with the remaining brownie pieces. Refrigerate until set, about 20 min. Just before serving, sift the cocoa powder overtop and serve.