Soak the basil seeds in 1 cup water until swollen and gelatinous, 15–20 minutes; drain and set aside.
Bring 4 cups water to a boil in a medium pot. Add the falooda sev and cook until translucent and tender, 3–5 minutes. Drain, rinse under cold water, and cut into 1–2 inch pieces; chill until needed.
Warm the milk in a saucepan over medium heat, stir in the sugar until dissolved, 2–3 minutes, then cool to room temperature and chill until very cold, 45–60 minutes.
Set out two tall (12–14 oz) glasses. Divide the rose syrup between the glasses (3 tbsp each), swirling some around the inside of each glass and letting the rest pool at the bottom.
Divide the cooked noodles evenly between the glasses, gently layering over the syrup.
Spoon a layer of the soaked seeds into each glass (about half in each), then slowly pour in the chilled milk to fill, leaving about 1 inch of headspace.
Top each glass with 1 scoop of kulfi and finish with chopped pistachios.
Serve immediately with a long spoon and a straw; the drink should be icy-cold and layered, with slippery noodles and softly crunchy seeds in each sip.