• Heat oven to 350ºF (163ºC) with rack set in middle position.

Crust

• Whisk together sugar, flour, rosemary, and salt. Using a spatula or wooden spoon, mix oil and 1 ½ tablespoons water into the flour until combined and mixture looks slightly crumbly.
• Crumble three quarters of the dough into the bottom of a 9-inch tart pan with removable bottom. Press dough into an even thickness lining the bottom of the pan. Crumble and scatter remaining dough around the edge of the pan; firmly press dough up and into the edge into an even thickness.
• Bake crust on a rimmed baking sheet until deep golden brown and firm to touch, 30–35 minutes, rotating halfway through. Transfer sheet to a wire rack and let crust cool completely.

Filling

• Sprinkle gelatin over 2 teaspoons water in a small bowl and let sit until softened, about 3 minutes. Microwave gelatin mixture until bubbling around edges and gelatin dissolves, 10–15 seconds.
• Add the cream, honey, amaretto, almond extract, and vanilla extract to bowl of a stand mixer fitted with the whisk attachment. With mixer running on medium-low, slowly add warmed gelatin mixture. Continue whisking until foamy about 1 minute.
• Increase speed to medium-high and whip just until stiff peaks form, 2–3 minutes (keep an eye on it, the addition of gelatin will make it whip much quicker.)
• Add mascarpone to a small bowl, add a few scoops of the whipped cream mixture to mascarpone and fold to combine (you may need to whisk a bit to incorporate completely—I just use the whisk attachment and do it by hand).
• Transfer mascarpone mixture to bowl with remaining whipped cream mixture and gently fold until combined.

Assembly

• Spread mascarpone cream evenly into cooled tart crust; refrigerate tart until filling has set a bit, about 30 minutes.
• Add blueberries to a small mixing bowl. Slightly warm 2 tablespoons honey in a very small microwave-safe bowl for about 8 seconds. Drizzle 1 tablespoon honey over blueberries and toss to coat. Scatter blueberries as desired over tart. Arrange blackberries and raspberries over top (I like to halve some of the berries for visual appeal).
• Using a pastry brush, dab remaining warmed honey over blackberries and raspberries.
• Chill assembled tart in refrigerator for 15 minutes before serving.
• To serve, remove outer ring of tart pan, slide a thin metal spatula between tart and and tart pan bottom, and carefully slice tart onto a serving platter or cutting board.