Melt 8 ounces of the white chocolate chips in a bowl over a double boiler or in the microwave. If using the microwave, melt for 30 second intervals, mixing the chocolate in between, until chips are fully melted.
Add the matcha and whisk until the matcha is incorporated.
Dip each strawberry in the matcha chocolate and place on a baking sheet lined with parchment or a Silpat. Place in the refrigerator for about 15 minutes until the chocolate has hardened.
Melt the other 3 ounces of chocolate chips in a small bowl using the same method as above. Dip the bottom tip of the matcha-covered strawberries in the white chocolate and place back on the baking sheet. Place in the refrigerator until the chocolate shell is hardened.