Trim and discard the rough ends of the artichoke hearts. Slice the artichoke hearts in half lengthwise. Place them cut side down on a paper towel, press them lightly to remove excess water, then turn them cut side up.
Spoon a small dollop of ricotta cheese on each artichoke half, add a Marcona almond in the middle, then wrap a strip of prosciutto around it. If needed, hold everything together with a toothpick.
Heat a large nonstick sauté pan over medium-high heat. Cook the wrapped bites on all sides until the prosciutto is crispy, 2 to 3 minutes total.
Transfer the bites to a serving platter and let them cool to room temperature. Drizzle with olive oil and balsamic vinegar and serve.