1. In a skillet, heat 1 tbsp oil and fry the garlic until fragrant. Add onion, basil and carrot in order and cook until soft. Season with the ingredient A and let it cool. Set aside.
2. Season the beef filet with kosher salt and pepper on all sides. In a large pan, heat 2 tbsp oil over high heat. Once the oil is hot, sear the fillet on all sides until well browned. Set aside.
3. Remove the beef filet from the pan and let cool. Once cooled, cover with the cooked vegetables from #1. Wrap filet with raw ham.
4. Tightly wrap the filet, using the plastic wrap and seal ends. Refrigerate for about 20 to 30min.
5. Pre-heat the oven to 200C. Roll out a sheet of puff pastry, unwrap the beef filet onto the puff pastry, then wrap until the ends meet. Cut off any extra puff pastry. You can decorate your puff pastry with the any excess.
6. Brush the surface with the beaten eggs. With a fork or a knife, score a decorative design onto the surface of the puff pastry as you like.
7. Bake for 40min or more until the puff pastry is golden brown and an instant-read thermometer inserted into the beef filet reaches about 60C (140°C) for medium-rare.
8. In the meantime, prepare the sauce. Add all the sauce ingredients into your food processor and process until smooth.
9. Slice into 2~3cm thick slices, gently transfer to serving plates and drizzle over some sauce, or serve on the side.