Place chicken breasts, smooth side down, between two sheets of plastic wrap and pound to 1/4 inches thickness.
Spread pesto evenly over chicken breasts, followed by cheese and sliced tomatoes. Sprinkle with salt and pepper to taste.
Roll up each chicken breast starting at one of the short ends. Place each chicken bundle seam side down in the Instant Pot, then secure the lid, making sure the vent is closed.
Using the display panel select the MANUAL or PRESSURE COOK function*. Use the +/- keys and program the Instant Pot for 5 minutes.
When the time is up, let the pressure naturally release for 5 minutes, then quick-release the remaining pressure.
Meanwhile, heat olive oil and butter in a nonstick skillet. When butter is melted, add panko, parmesan, 1/4 tsp salt and several grinds of pepper.
Cook, stirring constantly, until crumbs turn golden brown, then remove from heat immediately and continue to stir for 30 seconds to avoid burning.
When cooking cycle is complete, carefully remove the roll-ups from the pot, dip each in the skillet to coat the bottom with toasted crumbs, then place on individual serving plates.
Sprinkle remaining toasted crumbs over the top of the roll-ups, drizzle with marinara and top with basil ribbons.