Preheat oven to 400 degrees Fahrenheit, or to the temperature recommended on your package of puff pastry. Line a large baking sheet with parchment paper. Sprinkle a little flour on your pastry surface and, with a rolling pin, roll pastry sheet to approx 11-inches by 14-inches in size. Transfer pastry to baking sheet. With a butter knife, lightly score a 1/2-inch border around the edges, then fold the edge up and toward the center, pressing lightly, to create a neat border. Score the center lightly with a knife, taking care to not cut all of the way through (but if you accidentally do, it'll be okay). Bake until golden brown, about 10-12 minutes, or the time indicated on the package of puff pastry. Remove from oven and let cool completely.
Affix a stand mixer or hand mixer with the whisk attachment. In the bowl of the mixer or in a large bowl, beat the heavy whipping cream until soft peaks form. Scoop whipped cream into a medium bowl. To the bowl of the mixer or the large bowl, add the cream cheese, 3 tablespoons honey, lemon zest, lemon juice, and vanilla extract. Whip until smooth and a little fluffy, about 2 minutes.
Fold cream cheese mixture into whipping cream, gently stirring and folding just until blended. Pile the filling into the center of the cooled puff pastry tart shell and, with a butter knife. spread the filling gently toward the edges. Line the top with raspberries, bottoms up. Drizzle with remaining 3 tablespoons honey. Cut into squares and serve.
Notes
Make-ahead notes: Make the components ahead of time - bake the puff pastry, whip up the cream filling - then assemble right before it's time to eat. You'll want to keep the cream cheese filling in an airtight container in the fridge until about 20 minutes before it's time to assemble (be sure to give it that bit of time to soften at room temp so it's easy to spread).If you really want to assemble it a few hours ahead of time, it actually keeps rather well for even up to 4-5 hours, fully assembled, carefully covered, and refrigerated.