For the pesto, cook the broccoli rabe in a large pot of salted water until tender, about 7 minutes. Drain; transfer to a bowl of ice water to cool. In a small skillet over medium heat, cook the garlic with 1 tsp. of the EVOO, covered, turning occasionally, until the garlic is soft, about 10 minutes.
Drain the broccoli rabe; squeeze out the excess water. In a food processor, combine the broccoli rabe, garlic, pine nuts and mustard. Process until finely chopped. With the motor running, drizzle in the remaining 2 tbsp. EVOO. Transfer to a small bowl and stir in the Parmesan. Add water, 1 tbsp. at a time, until the consistency of a slightly thin pesto forms. Cover and chill up to 2 days.
For the pigs, preheat the oven to 350 degrees . In an 8x8-inch baking dish, fit the sausages snugly in 1 layer. Bake the sausages until browned and heated through, 15 to 20 minutes. Let cool. Trim the rounded ends off of the sausages.
Unfold one sheet of puff pastry and cut in half. Place on a lightly floured work surface. Arrange 2 sausages, end to end, across 1 long edge of the pastry. Spread1 tbsp. mustard in a thin line along the edge of the sausages. Brush some of the beaten egg along the other long edge. Roll up to enclose the sausage, pinching the dough to seal. Arrange seam side down on a parchment paper lined baking sheet. Repeat with remaining dough, sausages, mustard, and egg wash. Cover and refrigerate the egg wash. Cover and refrigerate the pigs until the pastry is cold, at least 1 hour or overnight.
Cut the pigs into 1-inch pieces and return to the baking sheet, seam-side down. Brush the top of the pastry with egg wash and sprinkle with the sesame seeds. Bake until the pastry is puffed and brown, rotating the baking sheet half way through, 25-30 minutes. Serve with broccoli rabe pesto for dipping.