Mix the olive oil, parsley, thyme, salt and pepper in a medium bowl. Add the shrimp and toss to coat. Let stand 30 minutes.
Add peeled boniato to cold water and cook until just tender. Drain and mash with heavy cream, butter, salt, and Parmesan cheese. Reserve for later and keep warm.
Combine the rum, tamarind, brown sugar, sweet chili sauce, ginger, and scotch bonnet pepper in a large saucepan and simmer on medium low heat for 15 minutes.
Mix cornstarch with the water until smooth and add to the sauce. Cook for another 5 minutes.
In saute pan, heat olive oil on medium heat and add shrimp. Cook for about 1 minute on each side or to when shrimp turns pink.
Add 1/4 of the rum sauce to the pan with shrimp and toss; cook for about 30 seconds. Remove from heat.
Saute vegetables in olive oil and allow them to be crisp, but tender.
To serve, pipe 2 to 3 ounces of the boniato mash in a martini glass, then arrange 4 shrimp around the rim of the glass with the tail out. Pile some of the sauted vegetables on top of the mash like a nest, then drizzle some of the sauce over. Garnish with a sprig of parsley.