For the caramel walnut cream: Place the white chocolate in a nonstick pan and melt it over low heat, stirring with a rubber spatula until completely melted. Let cook undisturbed until golden brown, 5 to 10 minutes. (The chocolate that is in contact with the bottom of the pan will caramelize and gain color.)
Take the pan off the heat and stir the chocolate together, pressing down and scraping against the pan until the chocolate is smooth and liquid again.
Bring the milk to a boil in a small saucepan.
Soak the gelatin sheets in cold water in a small bowl for 5 minutes. Squeeze the gelatin to remove excess water and stir it into the warm milk.
Add the white chocolate to a food processor. With the food processor running, stream the warm milk into the white chocolate, then stream in the heavy cream.
Pour out into a shallow 3-quart baking dish and stir in the walnuts. Cover the cream with plastic wrap pressed directly against its surface and refrigerate until firm, about 2 hours.
For the crust: Place the flour, butter, sugar and salt in a bowl and combine it with the tips of your finger until it resembles sand. Add the water and mix just until it comes together. (Do not overmix.) Wrap it in plastic and refrigerate for 1 hour.
Preheat the oven to 350 degrees F. Divide the dough into 6 even pieces, then use your fingers to press each piece into a 4-inch tart pan.
Prick the dough all over with a fork and bake until the edges look golden brown, 12 to 15 minutes. Let cool completely.
For the floral decoration: Fill the tart crusts with caramel walnut cream. Set aside.
Cut the flesh off the core of an apple in 4 pieces. Slice each piece super-thinly on a mandolin, so that each slice has a border of peel on it.
Place a piece of plastic wrap down on your work surface. Place one apple slice on one end of the plastic, cut-side facing you, domed side facing away. Then shingle the rest of the slices in a line from left to right. Brush them with some lime or lemon juice. Roll them up tightly until they take the size and shape of a rose. Place the apple rose on top of one of the tarts and open up the petals by loosening them with your fingers to create a flower that covers the entire surface of the tart.
Repeat with the remaining apples and tarts. Serve immediately.
Apple roses can be prepared up to 2 hours ahead. Drizzle assembled roses generously with lemon juice, wrap tightly in plastic wrap, and refrigerate, covered.