Let’s create this spectacular frozen dessert, stage by stage:

Part 1: Make the Homemade Mango Sorbet

1. Make Simple Syrup: Place the ¾ cup of sugar and ½ cup of water in a small saucepan. Cook over medium heat, stirring, just until the sugar completely dissolves. Remove from heat and set aside to cool completely.
2. Puree Mangoes: Place the peeled and seeded mango flesh into a food processor fitted with the steel blade. Puree until completely smooth. You should have about 5 cups of mango puree. (For an ultra-smooth sorbet, you can press this puree through a fine-mesh sieve or a food mill).
3. Combine and Chill Base: Combine the mango puree, the cooled simple syrup, ¼ cup fresh orange juice, and ¼ teaspoon kosher salt in a large bowl. Stir well. Cover and refrigerate until very cold, at least 2 hours or preferably overnight.
4. Churn Sorbet: Pour the chilled mango base into an ice cream machine and freeze/churn according to the manufacturer’s directions until it reaches a soft-serve consistency.

Part 2: Assemble the Ice Cream Bombe

1. Prepare Bowl and First Layer (Mango): Place a large 8-inch metal or glass bowl in the freezer for at least 30 minutes to get it very cold. Once the mango sorbet is freshly churned (or if using store-bought, softened slightly), place it in the chilled 8-inch bowl. Using a spatula, press the sorbet against the bottom and up the sides of the bowl to create an even layer, leaving a hollow center.
2. Form the Layer (Pro Tip): If you have a 6.5-inch nesting bowl, cover its outside tightly with plastic wrap and press it into the mango sorbet to create a perfectly even layer and a smooth, hollow center.
3. Freeze Layer 1: Place the bowl with the mango sorbet layer in the freezer for at least 30 minutes, or until firm. Once firm, remove the smaller 6.5-inch bowl (if you used one).

Part 3: Add Layers 2 & 3

1. Add Raspberry Layer: Spread the softened raspberry sorbet in an even layer on top of the firm mango sorbet layer. Again, you can use a smaller (e.g., 4.5-inch) plastic-wrapped nesting bowl to press it into an even layer with a new hollow center.
2. Freeze Layer 2: Freeze for another 30 minutes, or until the raspberry layer is firm. Remove the smaller bowl (if used).
3. Add Strawberry Core: Finally, spoon the softened strawberry ice cream into the remaining hollow center, filling the bowl completely. Smooth the top flat.

Part 4: Final Freeze and Serving

1. Freeze Solid: Cover the entire bowl tightly with plastic wrap. Freeze until the bombe is completely hard and solid, at least 4 hours or preferably overnight.
2. Unmold: When ready to serve, fill a larger bowl with warm water. Briefly dip the outside of the frozen bombe bowl into the warm water for just a few seconds (5-10 seconds) to loosen it. Run a thin knife or flexible spatula around the edge.
3. Place a chilled serving platter upside down over the bowl. Holding the bowl and platter firmly together, quickly invert them. The ice cream bombe should release onto the platter. Lift off the bowl. (If it doesn’t release, repeat the warm water dip briefly).
4. Serve: You can return the unmolded bombe to the freezer for a few minutes to firm up again before serving. Slice into wedges with a large, sharp knife (dipped in hot water for clean cuts) and serve immediately.

Patience with the multiple freezing steps is the key to beautiful layers!