Let’s bake these delicious, layered Strawberry Rhubarb Cheesecake Bars (I’ll complete the instructions based on standard baking methods for this type of bar):

1. Make the Raspberry Rhubarb Compote/Filling:

• In a heavy-bottomed saucepan, combine the 2 cups diced rhubarb, 1 ¼ cups raspberries (or strawberries, as per title), ⅓ cup + 1 tablespoon sugar, and the zest and juice of one lemon.
• Place the saucepan over medium heat. Bring the mixture to a hard boil, stirring occasionally. Let it simmer for 10 minutes, allowing the fruit to break down.
• In a small bowl, make a slurry by whisking the 3 teaspoons of cornstarch or tapioca starch with a tablespoon or two of cold water until smooth. Stir this slurry into the simmering fruit.
• Continue to cook for 3 minutes longer, stirring, until the mixture has visibly thickened into a jammy consistency.
• Remove the saucepan from the heat and stir in the ½ teaspoon of vanilla extract. Let the compote cool for at least 15 minutes.

2. Preheat Oven and Prepare Crust/Crumble Mixture:

• While the compote cools, preheat your oven to 350°F (175°C).
• Butter an 8×8-inch baking pan and line it with a parchment paper sling (with overhang on two sides for easy removal).
• In a large mixing bowl, whisk together the oat flour, rolled oats, quick oats, brown sugar, tapioca starch (1 tbsp), baking powder, sea salt, and cinnamon.
• Stir in the melted shortening or butter and mix well, using your hands if necessary, until no dry streaks remain and the mixture holds together in clumps.

3. Pre-bake the Crust:

• Take approximately ⅔ of the oat crumble mixture (about 220g as noted in original prompt) and press it firmly and evenly into the bottom of the prepared 8×8 baking pan. Use your fingers or the flat bottom of a glass to pack it down.
• Prick the base crust all over with a fork to prevent it from puffing up.
• Place the pan in the freezer for 10 minutes to chill and firm up the crust.
• Bake the chilled crust for about 15 minutes, or until it begins to lightly brown and is fragrant. Set the pre-baked crust aside to cool for about 10 minutes. Keep the oven on.

4. Make the Cheesecake Layer:

• While the base bakes, prepare the cheesecake filling. In a large bowl (preferably the bowl of a stand mixer), beat the room temperature cream cheese on medium speed until completely smooth and no lumps remain.
• Mix in the 75g of granulated sugar. Then, mix in the Greek yogurt, heavy cream, and 1 teaspoon vanilla extract until combined.
• Beat in the 1 ½ large eggs (or equivalent weight/volume) on low speed, just until incorporated.
• Lastly, sift the 1 ½ tablespoons of cornstarch over the top of the mixture and mix on low speed until just combined. Do not overmix the cheesecake filling.

5. Assemble and Bake the Bars (Inferred Step):

• Pour the prepared cheesecake filling evenly over the slightly cooled, pre-baked crust. Smooth the top with a spatula.
• Spoon the cooled raspberry rhubarb compote over the cheesecake layer. You can dollop it randomly or gently swirl it with a knife for a marbled effect.
• Take the remaining ⅓ of the oat crumble mixture and sprinkle it evenly over the top of the fruit and cheesecake layers.
• Place the baking pan in the preheated oven. Bake for 40-50 minutes. The bars are done when the edges are set, the cheesecake appears mostly set with only a slight wobble in the very center, and the crumble topping is golden brown.

6. Cool and Chill Completely (Crucial Step – Inferred Step):

• Turn off the oven and let the bars cool in the oven with the door cracked for about 30 minutes. Then, remove the pan and let it cool completely to room temperature on a wire rack (this will take a couple of hours).
• Once completely cool, cover the pan with plastic wrap and transfer it to the refrigerator to chill for at least 4 hours, or preferably overnight. This step is essential for the cheesecake layer to set completely, ensuring clean, sturdy bars when you cut them.

7. Slice and Serve (Inferred Step):

• Once thoroughly chilled and firm, use the parchment paper overhang to lift the entire block of bars out of the pan and onto a cutting board.
• Using a large, sharp knife (wiped clean between cuts), slice into squares or rectangles. Serve chilled.

Patience during cooling and chilling is key for perfect cheesecake bars!