Place the potatoes in a large saucepan with kosher salt and enough water to cover. Bring to a boil and then reduce to a simmer. Split jalapenos, remove seeds and white membranes and drop in boiling water with potatoes; blanching about 90 seconds. Remove, cool and mince or peel and mash.
Cover potatoes and simmer for about 20 minutes, cooking until the potato are done. Drain and rinse pot and potatoes in hot water, then place pot back onto warm stove to dry.
While the potatoes are cooking, warm the half & half in a second saucepan.
Mash the hot potatoes, slowly stirring in the warm milk and soft butter as needed. Add about 1/2 tsp of the jalapeno, grated cheese and chives. Taste and adjust with salt, pepper and more jalapeno as desired.