Melt 1 Tbsp of butter in a large skillet (with a tightly-fitting lid).
Add the onion and saute' until tender, stirring, which will take about 5 minutes.
Stir in the broth, cover skillet, and heat to boiling.
When boiling, stir in the rice, diced carrot, and garlic, then cover tightly and cook over medium-low heat for 15 minutes or until all liquid is absorbed.
When rice has cooked for 15 minutes, melt the remaining 3 Tbsp of butter, uncover the rice and drizzle 2 Tbsp of the butter evenly over the top.
Turn the heat to high, and using a large spoon or spatula, press down on the rice.
Spread a layer of the zucchini slices over the top of the rice; drizzle with the remaining Tbsp of butter; sprinkle with salt and pepper to taste, then the grated Parmesan cheese.
Cover the skillet tightly and cook over medium heat for 10 to 15 minutes- the aim is that the layer of rice on the bottom of the pan is toasted a rich golden brown; if you have a gas stove as opposed to electric, times and temperatures may vary to achieve the desired texture.
As the rice is cooking, you will be able to smell the aroma: you can lift the lid and the rice at the edge of the skillet to check the progress.
Not all the rice will become crunchy- there will be a nice mixture of textures and tastes; serve a bit of the crunchy rice layer with every spoonful.