Remove the cream cheese from the refrigerator and allow it to soften at room temperature.
In a mixing bowl, combine the milk, strawberry jam, cornstarch, and glutinous rice flour. Whisk until smooth.
Strain the mixture through a fine-mesh strainer into a microwave-safe bowl to remove lumps.
Cover the bowl with microwave-safe plastic wrap and poke about 12 small holes in the wrap with a toothpick.
Microwave the mixture on high power for 3 minutes, or until fully cooked. Insert a toothpick into the center; if it comes out clean, the mochi dough is done.
Carefully remove the bowl from the microwave. Add the butter and mix with a nonstick spatula until fully absorbed into the dough.
Allow the mochi dough to cool completely at room temperature. Avoid touching the dough while warm.
In a mixing bowl, whip the softened cream cheese and granulated sugar using a hand mixer for about 2 minutes until fluffy.
In a separate bowl, whip the heavy cream and vanilla extract until stiff peaks form.
Fold the whipped cream into the cream cheese mixture and mix on low speed until fully combined. Transfer to a piping bag if desired.
Wash, dry, and dice the strawberries. Mix with strawberry jam if using. Set aside.
Once cooled, knead the mochi dough by stretching and folding it for about 5 minutes until smooth and elastic.
Divide the dough into 6 equal portions.
Wrap a rolling pin with plastic wrap to prevent sticking and roll each dough portion into a 5-inch circle.
Dust one side lightly with glutinous rice flour and place the dough into a sphere mold with the floured side facing down.
Pipe cream filling into the center, add diced strawberries, then top with more cream filling.
Pull the edges of the dough together and pinch tightly to seal.
Flip the daifuku over so the smooth side faces up.
If not using a sphere mold, roll the dough into squares and fold into pillow shapes around the filling.
Garnish each strawberry daifuku with a whole strawberry on top.
Serve immediately or refrigerate in an airtight container for up to 3 days.