In a small bowl, gently toss raspberries with sugar and a light drizzle of oil. Spread on a small, rimmed baking sheet and bake 5 to 7 minutes, just until raspberries are softened and fragrant.
Remove from the oven and scoop into a fine sieve placed over a bowl to drain juices. Let sit while you prepare the dough, then toss the juice and save the raspberries.
BISCOTTI:
In a large bowl, use an electric mixer to cream together butter and sugar until light and fluffy. Beat in the eggs one at a time, mixing well after each one. Stir in the drained roasted raspberries and 2 teaspoons lemon zest until well blended.
In a separate bowl, whisk together the flour, baking powder and salt; stir into the batter. Last, gently stir in the raspberry jam until almost incorporated. Cover and refrigerate for about 10 minutes.
Preheat the oven to 350℉ Lightly grease two cookie sheets.
Divide the dough into four equal parts. Form each piece of dough into a 12 -nch long log shape on a lightly floured surface. Place two logs onto each cookie sheet, and pat down until they are about 3 inches wide. There should be at least 2 inches of space between each log. Gently press pieces of cut raspberries randomly on the top of each of the logs. Sprinkle remaining lemon zest on top, gently patting into the top of the dough.
Bake for 30 minutes until firm but not crisp. Remove from oven and cool for 10 minutes. Keep the oven on.
Place the biscotti loaves on a cutting board. Use a serrated knife to cut into ¾-inch wide slices. Return the slices to the baking sheets cut-side down.
Bake an additional 8 minutes, then turn the cookies over, and bake for 8 minutes more, or until lightly toasted on each side. Watch the biscotti closely. It should be dry and lightly browned. If you prefer crispier biscotti, you may wish to extend the baking time a little bit on each side.