Place the whole hazelnuts and 1 tablespoon oil in a food processor and process until a smooth paste is formed, 4-5 minutes, scraping down sides if necessary.
Add confectioner's sugar, cocoa, chocolate, remaining tablespoon of oil and salt and process until smooth.
Transfer to a container and chill until mixture has hardened, at least 2 hours and up to 8.
Preheat oven to 300°F.
Line a large cookie sheet with parchment paper and reserve.
Place egg whites in the clean, dry bowl of a stand mixer with cream of tartar and salt.
Beat until foamy, stop mixer and add sugar and vanilla, then beat on high until mixture forms stiff peaks, 4-5 minutes.
Fold in toasted hazelnuts.
Pipe 1 tablespoon meringue onto parchment.
Using a small melon baller, scoop 2 teaspoons chocolate mixture and place in center of meringue.
Top with an additional 2 teaspoons meringue, completely covering chocolate (see photo).
Repeat with additional meringue, leaving about 2 inches of room between cookies (you will have a little extra chocolate filling, perfect at room temperature for spreading on matzo).
Bake until meringues have set and edges are very lightly browned, 25-30 minutes, then remove from oven and cool completely.