Pre-heat oven to 375°F
In a large pot, heat ¼ cup butter over low heat. Add onion and cook, stirring, 3 to 4 minutes. Stir in garlic, and cook for another 2 minutes.
Add in chopped tomatoes and red peppers, sprinkle with salt and pepper (about ¼ tsp each), increasing the heat to medium-high, and let cook for 10 minutes.
Pour in ¼ cup of the milk, reserving ¼ cup. Mix the remaining ¼ cup of milk with 2 tbsp flour and stir. Pour into the pot.
Add 1 tsp sweet paprika, oregano leaves (stem removed), and 2 of the basil sprigs (stem removed). Reduce the heat to medium, with a low simmer for another 30 minutes.
While the sauce is cooking, slice the potatoes, zucchinis, and eggplants into ½ cm thick rounds using a mandolin or a steady hand.
Pour olive oil on the bottom of a round 9 inch glass pie dish and coat surface evenly.
Once the sauce is done cooking, strain it so to separate the liquid and the chunky vegetables. Pour the chunky part into the bottom of the pie dish, filling it halfway up, or less. Do not discard liquid portion, set aside.
Take one of each type of zucchini, eggplant, and potato coin and start stacking them in your hand until you can’t hold any more. Then lay them horizontally in the dish and start to create a circular pattern going inward. Repeat this process until the dish is filled.
Drizzle the vegetables with olive oil, and season with salt and pepper.
Pour the remaining liquid portion of the sauce over the vegetables, making sure to leave at least 1 cm clearance at the top. Cover with foil and bake for 30 minutes.
Remove foil after 30 minutes and continue cooking for another 45 minutes.
Once done, remove from oven and let cool, 15 minutes.
Garnish with remaining basil leaves.