try looking up a "streusel" topping. largely butter, dark/muscovado sugar, flour and some sort of nut (i used to make one with toasted pecans to top a yoghurt-based fluffy tray bake with strawberry pieces)
and im guessing that pistachio creme situation is a "diplomat" (whipped cream fortified with gelatine). You could make a diplomat with the inclusion of pistachio paste + a few drops of extract (paste has richness but not all that much flavour) and most likely a drop or 2 of light green dye, since pistachio paste is generally brown.
If you're garnishing with rosemary, does this suggest some rosemary in the filling?
My uneducated guess was that this was in the style of a no-bake cheesecake. My mom would do this with cream cheese, sweetened condensed milk and powdered gelatin. Then perhaps a crumbly cookie base as it seems to have more structure to my eye than a struesel might. like a molasses spice cookie.
If savory, then perhaps the crust is toasted bread crumb/nut crust although the smooth baked upper crust edge belies that idea. That upper edge is really throwing me off.
Tell us more about the source of that picture. That might give us some context clues.